Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Mr Andrew on 10/12/2007 21:34:40
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As far as I can tell, using various resources, the best modern theories can do to predict the direction that light has when it is emitted from an atom is to say that on average, with a large sample, it is emitted omnidirectionally. But, probability is only useful for describing what you don't yet know...for example, in a coin toss, the probability of a heads is 1/2 because you don't know what will happen yet. Why it happens when it does is dependent on intitial and environmental conditions; if you knew all of those, you would be able to predict absolutely whether the coin would come up heads or tails. What causes light to move in this direction instead of that when it leaves the atom? Could it be the magnetic dipole moment of the atom (or some other vector singular to that atom)? If I were to take a magnetized monofilament and apply a voltage to it would it emit most of its light in one direction (most of the magnetic dipole moments of the wire would be aligned in the same direction)?
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Even if you precisely know everything about an atom and its environment, you still don't know exactly where the radiation is emitted on a quantum level. This is because quantum mechanics describes the probability of emission in various directions, and unlike the coin, these probabilities are fundamental to the theory--you can't get rid of them by knowing more about the atom.
If you're talking about a larger scale, any detector you use to figure out the direction of the light is going to have to average over some short period of time. Because the atom itself is jiggling about so fast, you're going to average over a whole bunch of atomic orientations. Even if the atom is emitting in a particular direction, you won't be able to see it because of the averaging.
As far as I know, if you could line up atoms in some direction, such as you propose, you should be able to give the field a directionality. In a perfect world, you could go as far as the quantum limits.
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It seems quite reasonable to think that an atom radiates light in the same way that a small antenna radiates (longer) radio waves because of the size relative t a wavelength. Classical theory forbids an omnidirectional radiator; the 'most omnidirectional' radiator is a short dipole / doublet and its pattern is like a ring doughnut; it has nulls at the poles. The problem with verifying this is that it is hard to know the allignment of any particular atom. A has been said above, the net result of a lot of atoms is omnidirectional.
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A better approximation to an omnidirectional radiator can be achieved with a quadrifilar helix array.
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It seems quite reasonable to think that an atom radiates light in the same way that a small antenna radiates (longer) radio waves because of the size relative t a wavelength. Classical theory forbids an omnidirectional radiator; the 'most omnidirectional' radiator is a short dipole / doublet and its pattern is like a ring doughnut; it has nulls at the poles. The problem with verifying this is that it is hard to know the allignment of any particular atom. A has been said above, the net result of a lot of atoms is omnidirectional.
Is not the exception to this the case of a laser. where the emission only happens if it is lined up with the incoming stimulating radiation?
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It seems quite reasonable to think that an atom radiates light in the same way that a small antenna radiates (longer) radio waves because of the size relative t a wavelength. Classical theory forbids an omnidirectional radiator; the 'most omnidirectional' radiator is a short dipole / doublet and its pattern is like a ring doughnut; it has nulls at the poles. The problem with verifying this is that it is hard to know the allignment of any particular atom. A has been said above, the net result of a lot of atoms is omnidirectional.
Is not the exception to this the case of a laser. where the emission only happens if it is lined up with the incoming stimulating radiation?
This is stimulated emission. You're right--it is directional. It's a quantum mechanical effect that happens when incoming light strikes an atom that has been "excited" (i.e. it has absorbed energy from somewhere.) When struck by light, there's an increased probability that the atom will emit light in the same direction and in phase with the incident light.
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If you magnetized the wire enough, could you show that if a significant percentage of the light emitted was in a specific direction that, dipole moment affected emission direction?...or can you show this with Quantum Theory without running tests?
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It seems quite reasonable to think that an atom radiates light in the same way that a small antenna radiates (longer) radio waves because of the size relative t a wavelength. Classical theory forbids an omnidirectional radiator; the 'most omnidirectional' radiator is a short dipole / doublet and its pattern is like a ring doughnut; it has nulls at the poles.
If I remember well, the fundamental state of the hydrogen atom (or other orbitals of other atoms) has net orbital angular momentum = 0. How can you see a radiating dipole, in that case? Directionality in the photon emission of an atom is not possible in such cases.
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As far as I can tell, using various resources, the best modern theories can do to predict the direction that light has when it is emitted from an atom is to say that on average, with a large sample, it is emitted omnidirectionally. But, probability is only useful for describing what you don't yet know...for example, in a coin toss, the probability of a heads is 1/2 because you don't know what will happen yet. Why it happens when it does is dependent on intitial and environmental conditions; if you knew all of those, you would be able to predict absolutely whether the coin would come up heads or tails. What causes light to move in this direction instead of that when it leaves the atom? Could it be the magnetic dipole moment of the atom (or some other vector singular to that atom)? If I were to take a magnetized monofilament and apply a voltage to it would it emit most of its light in one direction (most of the magnetic dipole moments of the wire would be aligned in the same direction)?
The directionality of a beam of light is generated by the media in which light propagates. Example: a (small) lamp spreads light in all directions; you put it in the focal point of a thin lens and the light exit parallel from the lens; or you could simply put, very far from the lamp, a screen with a small hole in it; light exiting the hole is approximately plane and so diverges a little. Sun's light, for ex., comes from a very far distance, so this effect is more apparent.
In the case of lasers, as it's been said, it's exploited stimulated emission, which has also the peculiarity to be in the same direction of the stimulating radiation; furthermore, the laser has a resonant cavity, which select the radiations emitted along the laser's axis.
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A better approximation to an omnidirectional radiator can be achieved with a quadrifilar helix array.
But that would be quite large (?), perhaps a half wavelength or more. An atom is much less than quarterwavelength of light. Also, I have a feeling that your array produces elliptical polarisation - it's a bit special.
Yes, a laser is highly directional BUT only because the individual radiators are cophased (the mechanism doesn't really matter) and the effective aperture is many many wavelengths. Where you have a lot of individual atoms, there is no coherence and the statistics should give you omnidirectional radiation.
I know radio isn't a favourite wavelength for all you photon fans but basic antenna calculations tell you an awful lot about what to expect.
f I remember well, the fundamental state of the hydrogen atom (or other orbitals of other atoms) has net orbital angular momentum = 0. How can you see a radiating dipole, in that case? Directionality in the photon emission of an atom is not possible in such cases.
Ah yes, good point but the atom, in its established state, is not radiating anything. It only radiates whilst changing state. It's anybody's guess what is happening whilst the states are in the process of changing and the energy is being radiated. My point is that it is increasingly difficult to produce a highly directional pattern from a tiny radiator. The pattern may not be that of a short dipole but it is unlikely to have a narrow 'beam', although it could have nulls in odd directions.
A model involving photons 'being fired off in specific directions' would require a radiating aperture of millions (or even ten to the power an awful lot) of wavelengths - that sounds almost as dodgy as needing to involve quantum entanglement to explain how a single photon can only interact with one atom in one direction.. If the photon spreads out at all on its journey, then it could encounter two atoms, within its influence and, so, would have to choose which one was to absorb it. The QM thing would have to happen anyway.
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Consider one atom in a closed and isolated system. It is in an excited state. Then it emits a photon of light and it settles into its ground state. The photon has to be emitted in a direction. How is that direction decided? If you think of the electron as a standing wave about the nucleus (which explains the quantization thing because standing waves have modes of discrete energy levels) then it is everywhere around the nucleus at once (as QM postulates). The only vector associated with this atom (which I can think of) is its dipole moment (related to orbital angular momentum of the electron). Would this somehow affect the radiation direction of the photon?
If you take the equation E2 = (mc2)2+(pc)2 you can see that p (momentum) is directly proportional to E (total energy). If an electron loses energy when it emits a photon, its momentum goes down. That means that by conservation of momentum (assuming the electron's momentum vector stays oriented in the same direction through the whole process) that the photon's momentum vector would have to point in the same direction as the electron's (to make up for the lost momentum of the electron). The question is, where does p point. Is it along the dipole moment? Can you align a group of atoms' p vectors and create a directional light emitter?
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Consider one atom in a closed and isolated system. It is in an excited state. Then it emits a photon of light and it settles into its ground state. The photon has to be emitted in a direction.
Why? Photons don't have Nadelsstrahlung (aciform propagation)
How is that direction decided? If you think of the electron as a standing wave about the nucleus (which explains the quantization thing because standing waves have modes of discrete energy levels) then it is everywhere around the nucleus at once (as QM postulates). The only vector associated with this atom (which I can think of) is its dipole moment (related to orbital angular momentum of the electron). Would this somehow affect the radiation direction of the photon?
If you take the equation E2 = (mc2)2+(pc)2 you can see that p (momentum) is directly proportional to E (total energy)
??. If an electron loses energy when it emits a photon, its momentum goes down. That means that by conservation of momentum (assuming the electron's momentum vector stays oriented in the same direction through the whole process) that the photon's momentum vector would have to point in the same direction as the electron's (to make up for the lost momentum of the electron). The question is, where does p point. Is it along the dipole moment? Can you align a group of atoms' p vectors and create a directional light emitter?
If you can tell me which was the electron's momentum before and after the emission...(hint: look for Heisenberg Uncertainty Principle). You have to remember that even if you knew energy exactly, that formula only gives you the modulus of the momentum, not its direction!
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How do you define 'direction'of a photon?
What is the accuracy with which you would define the direction?
When you are talking of a distant galaxy and a photon finding its way to an atom in that galaxy. This represents a fantastically narrow beam in which to define the path of this photon, which implies an amazing mechanism with unbelievable directivity. Over what area would you expect the target system to be affected by a passing photon?
What sort of mechanism, what sort of 'aperture' would you need, bearing in mind that a photon would be subject to diffraction (they can be shown to be subject to the same degree of diffraction that affects a conventional wave of the same frequency).
As soon as you consider a distance of more than a few atoms' length, this must be considered and you have to stop talking about the dreaded little bullets. The region affected by a photon just has to be very large.
On another angle and, to aid understanding:
I wish that people would consider systems other than the introductory School Hydrogen Atom model. Many photons that we observe have not come from such a system. They come from gases under pressure and from condensed matter. You can't discuss the photon in terms of orbits and electrons. Their emission may not involve electronic states at all; rotational and vibrational states of molecules must be allowed for in any theory. You must also be prepared to talk about energy bands and not just energy levels. Your theories must explain radio antennae and nuclear gamma decay, at the remote ends of the spectrum.