Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Andrejs Skuja on 24/11/2010 01:30:03
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Andrejs Skuja asked the Naked Scientists:
Hi Chris,
I have a query I'd love answered if possible.
I was recently posed the question, 'Why do our solar system's planets sit on a flat plane'. I understand this is due to the conservation of angular momentum. Upon discovering this the first image to jump to mind was of an atom with it's electrons zipping around it in random trajectories not adhering to a single plane. Why does the law that binds our solar system seem not to apply to atoms, or is my view based on flawed cartoons from my childhood? (Up and at 'em, Atom Ant!)
Thanks very much,
Andrejs Skuja
What do you think?
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Excellent question! Electrons in atoms do have angular momentum. The difference is their orbits are these fuzzy quantum clouds called orbitals rather than nice classical orbits like the planets. These orbitals aren't random, and they do have different shapes which are specified by their energy and angular momentum. Without going into details, there are some pictures here: http://en.wikipedia.org/wiki/Atomic_orbital#The_shapes_of_orbitals
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Isn't it also something to do with the idea that when not being observed the electron is a standing wave rather than an orbiting particle?
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Isn't it also something to do with the idea that when not being observed the electron is a standing wave rather than an orbiting particle?
Is it that a standing wave is the radiation energy resultant of the obiting partical?
Electrons do have a mass where a standing wave is radiation containing photons I think ?
Or is there a photon to partical swapping action here?
Is my thinking incorrect here?
Excellent question! Electrons in atoms do have angular momentum. The difference is their orbits are these fuzzy quantum clouds called orbitals rather than nice classical orbits like the planets. These orbitals aren't random, and they do have different shapes which are specified by their energy and angular momentum. Without going into details, there are some pictures here: http://en.wikipedia.org/wiki/Atomic_orbital#The_shapes_of_orbitals
From my minds eye, deriving from that site, am I correct to say, that the electrons are revolving around the nucleus on a plane and the plane is also revolving on an concentric axes, centrally pivoting on the nucleus?
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Maybe that the size of the universe prohibits any reference point to permit use to see the solar system is also in a wabble of sorts? Maybe the duration of the wabble is to extreme
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Isn't it also something to do with the idea that when not being observed the electron is a standing wave rather than an orbiting particle?
Yeah. That's basically exactly what's happening, and waves can have angular momentum just like particles can. Interestingly, in order for light to cause an electron to jump from one energy level to another, the photon that gets absorbed or emitted has to have the right angular momentum so that total angular momentum of the energy level + photon is conserved.
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From my minds eye, deriving from that site, am I correct to say, that the electrons are revolving around the nucleus on a plane and the plane is also revolving on an concentric axes, centrally pivoting on the nucleus?
No, that's not quite correct. The electron is smeared out over the whole orbital shape at one instant. Part of quantum mechanics says that you have to use this smeared-out model and that you simply can't use the model of a particle zipping around an orbit. Angular momentum determines the shape of the orbital, though.
Both the planet and the electron have angular momentum, but the electron behaves like a wave that's smeared out over the whole orbital at once, while the planet behaves like a mass that takes up only one point on the orbit at any time and moves around the orbit as time goes on.
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On the subject of an electron that jumps from one energy level to another, the thing I have difficulty getting my head round is that one cannot think of it as being anywhere while it is making the transition. What happens to the angular momentum during the transition?
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I was recently posed the question, 'Why do our solar system's planets sit on a flat plane'. I understand this is due to the conservation of angular momentum. Upon discovering this the first image to jump to mind was of an atom with it's electrons zipping around it in random trajectories not adhering to a single plane. Why does the law that binds our solar system seem not to apply to atoms, or is my view based on flawed cartoons from my childhood? (Up and at 'em, Atom Ant!)
Conservation of angular momentum still holds, but microscopic objects cannot have a precise trajectory, or this would violate Heisenberg uncertainty principle; in the microscopic domain the exact position and velocity of a particle are replaced by an entire function of space x and time t, called "wavefunction" which square modulus gives you the probability per unit volume to find the particle in a region of space around x at the time t. You cannot know its position and velocity, and so its trajectory, better than this, and not because of instrumental inefficiency, but because of theoric reasons.
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On the subject of an electron that jumps from one energy level to another, the thing I have difficulty getting my head round is that one cannot think of it as being anywhere while it is making the transition. What happens to the angular momentum during the transition?
During the transition it's in both A and B. I read this somewhere after someone asked how long the transition takes. There's a finite but very short time it spends straddling the two states. (If it instantly hopped from one to the other, it would move faster than the speed of light.) If you try to measure its angular momentum during the transition, you'd find it would either be in state A with some probability or state B with some other probability.
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On the subject of an electron that jumps from one energy level to another, the thing I have difficulty getting my head round is that one cannot think of it as being anywhere while it is making the transition. What happens to the angular momentum during the transition?
Angular momentum, in the form of "spin" is transferred to or from the photon.
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On the subject of an electron that jumps from one energy level to another, the thing I have difficulty getting my head round is that one cannot think of it as being anywhere while it is making the transition. What happens to the angular momentum during the transition?
Angular momentum, in the form of "spin" is transferred to or from the photon.
The photon can also have angular momentum on top of spin. For example, certain beams tend to "rotate," which gives the photons angular momentum.
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If an antenna is receiving a circular polarised signal is a torque transferred to it albeit very small?
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If an antenna is receiving a circular polarised signal is a torque transferred to it albeit very small?
I would propose this as "The question of the year".
Good question!
(I mean, it surely has an answer, but I don't know it).
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Thanks for the responses. A thought, which may well be completely iconoclastic, is struggling to gain a foothold in my mind. It concerns the positions of quantum objects, and looking back at the start of this thread, I think it may be a somewhat off subject, so I shall think about it a bit and, perhaps, start a fresh thread. [8D]
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If an antenna is receiving a circular polarised signal is a torque transferred to it albeit very small?
I would propose this as "The question of the year".
Good question!
(I mean, it surely has an answer, but I don't know it).
I agree. It's certainly worth starting a new topic.
Syhprum, would you like to do that? We don't want to pinch your question.
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If an antenna is receiving a circular polarised signal is a torque transferred to it albeit very small?
I would propose this as "The question of the year".
Good question!
(I mean, it surely has an answer, but I don't know it).
The answer is almost certainly yes. Circular polarization is a relatively small effect (and is closely related to photon spin). Beams with what's called angular momentum impart much more angular momentum to objects they strike.
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If an antenna is receiving a circular polarised signal is a torque transferred to it albeit very small?
I would propose this as "The question of the year".
Good question!
(I mean, it surely has an answer, but I don't know it).
The answer is almost certainly yes. Circular polarization is a relatively small effect (and is closely related to photon spin). Beams with what's called angular momentum impart much more angular momentum to objects they strike.
But it sounds strange to me: the electric and magnetic field are still oscillating along a single direction and with respect to the same point; to have a torque there should be two field vectors not applied in the same point and along different action lines. [???]
How can this happen in our case?
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I guess it isnt oscillating back and forth along 1 dimension.
looks like the electric field must be rotating
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I guess it isnt oscillating back and forth along 1 dimension.
looks like the electric field must be rotating
By rotation, what is meant? Their is a relative case of rotation, but I am not sure what context you are proclaiming this in.
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I guess it isnt oscillating back and forth along 1 dimension.
looks like the electric field must be rotating
Of course... [:)]
What I meant is: it oscillates back and fort along a direction + this direction rotates, but however it oscillates in a direction; the electric (or magnetic) vectors don't create a couple. Nonetheless, angular momentum conservation implies there must be a torque...
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I would like to return to the original question. The fact that the solar system (and galaxies) tend to occupy a flat plane is nothing to do with the conservation of angular momentum. This is always conserved for orbits in any direction and at any scale right down to the absolute limits. This is a requirement (via Noether's theorem) for physical laws to be consistent whatever direction you are facing.
The reason for the flat disc like structures is due to The multi-particle dynamics of collapsing rotating objects containing angular momentum. If many bodies are orbiting in random orbits of all shapes and directions they will occasionally collide link up break up and share orbital energy and change their orbits sometime bodies will gain a lot of energy and be ejected from the system. If bodies are orbiting in a flat plane in orbits that are close to being circular the probability that they will collide at high speed is very greatly reduced so given time a flat disc structure is likely to develop. There is also a suggestion that the extremely weak "gravitomagnetic" forces also act on orbits in a way that helps this disc structure to form and stay stable.
The charge and electromagnetic forces on a conceptual electron particle allow the formation of the stable three dimensional orbital patterns even if the individual paths of electrons in this structure are not observable.
As to the question of the reaction of an antenna to the receipt of a signal the reaction of atoms when emitting or absorbing high energy photons is observable and the reaction of a mirror reflecting light is observable so an antenna receiving radio waves will react to the signal it is receiving so there will definitely be a reaction in the opposite direction to the signal coming in. Next we have the question if this is a circularly polarised signal with the matched circularly polarised antenna. will there be a torque on the antenna? I cannot think of an equivalent experiment at high energy where this sort of waves could be generated and reactions measured but by extending the analogy my guess is yes there will be a torque.
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Next we have the question if this is a circularly polarised signal with the matched circularly polarised antenna. will there be a torque on the antenna? I cannot think of an equivalent experiment at high energy where this sort of waves could be generated and reactions measured but by extending the analogy my guess is yes there will be a torque.
If you tune the energy of your light beam way down, you're basically hitting the antenna with single photons, all with the same spin. The spin would impart angular momentum onto the antenna. I suspect you could do a similar thing by taking electrons, for example, all with spin +1/2, and sending them at a detector. It's probably not practical, though.
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I thought it was a relatively trivial matter but enter it as a new question by all means (I am boosting up the mounting of my weather satellite antenna) just in case!
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Let's calculate the angular momentum of circularly polarized radio wave that has frequency of 1 Hz, and energy of 1 J.
The number of photons is the inverse of planck's constant.
Each photon has angular momentum of planck's constant / 2 pi
So answer is 1 / 2*pi Nms (0.16 Newton meter seconds)
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So ... let's take 50 left circularly polarized photons, and 50 right circularly polarized photons. Now we mix these photons together. Now what we have is linearly polarized light.
Any objections?
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Hey now I know. Elliptically polarized photon, where the ellipse is very long and thin is about the same as linearly polarized photon!
I see, Wikipedia says the same. Well I invented it anyway.
So ... there are no non-polarized photons.
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So, on the left we see linearly polarized light.
On the right we see circularly polarized light, I guess?
(both lights are made of two photons)
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I would personally drop the term photon, since properly describing a beam of light in terms of photons is a complicated process, but the basic idea is right: a linearly polarized beam of light can be thought of as the addition of a left-hand circularly polarized and a right-hand circularly polarized beam. Similarly, a circularly polarized beam of light can be thought of as the addition of two linearly polarized beams (in this case you have to add phase to one beam, which basically means you shift it by 1/4 wavelength with respect to the other beam.
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Actually photons have 'spin', other name for this 'spin' could be 'elliptical polarization'
So, some photons have very elongated spin, some have quite round spin.
This is how light that is made of one photon can be polarized in all the same ways that light made of two photons can be polarized.
Now doesn't this just sound very very much wrong:
So, some photons have very elongated spin, some have quite round spin.
Well, anyway, photons have spins with different elongations pointing at different directions.