Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: graham.d on 10/08/2010 12:36:01
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I have wondered for a long time why the wavefunction associated with a photon is a tangible and measurable change in an electromagnetic field whereas (all?) other particles have a less tangible probability amplitude associated with them. An example is an electron which exhibits interference and diffraction but for which the wave function appears as just an abstract probability amplitude.
Are there any other particles for which the wavefunction is a sinusoidal change in a field? If not, can any insight be drawn from this?
If a Higgs Boson is found, would its associated wavefunction be tangible gravity waves?
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I have wondered for a long time why the wavefunction associated with a photon is a tangible and measurable change in an electromagnetic field
You are wrong, the wavefunction associated with a photon is not the em field, even if you can often use this description to compute something.
However it's difficult simply to define a wavefunction for a photon, since the fact it's massless makes it difficult to define a position operator for it. Unfortunately I didn't studied QED so you have to ask others for a more complete answer [:)]
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I didn't say the wavefunction WAS the field but that it is somehow associated with the changing field to give the same results - interference, diffraction etc. I wanted to keep the essence of the question simple but an associated question would be:
As the photon mediates the em force, the graviton mediates the force of gravity and the pion the nuclear force (I think this is right but it is from memory), do these particles have tangible waves in their associated fields that produce identical results to a probability amplitude?
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Ah yes--I've studied this a bit. The classical sinusoidal EM wave turns out to be a description of a particular kind of quantum state called a coherent state. This is a particular way of combining photons such that they add up to a sinusoid. The coherent state is a particular way of combining 1 photon + 2 photons + 3 photons + 4 photons + ... with a certain probability of finding a certain number of photons if you try to measure them. They actually add up to a sinusoid with a bit of "width" at any point, due to uncertainty relations, but if there's enough energy (i.e. the amplitude of the sinusoid is big enough), the width doesn't matter, since its small compared to the amplitude. You can construct non-sinusoidal types of EM fields too, which are generally called non-classical, since they have properties you can't generally describe with classical electromagnetic theory: a single photon state is one example. Mathematically, this comes about by trying to construct a state of a quantum harmonic oscillator that looks like a classical harmonic oscillator, which oscillates sinusoidally.
Now, the interesting (and confusing) point is that the classical EM wave field ALSO has a particle-like description: rays. This is because by an amazing turn of luck, the equations governing light beam propagation have the same mathematical form as those of quantum mechanics--and the approximation that lets you get classical mechanics from quantum mechanics (if you're looking at large objects compared to the wavelengths of your particles) also lets you get ray optics from wave optics (when the wavelength of your field is much smaller than any physical dimension in your system). In fact, Schrodinger developed his famous QM equation by looking at how ray optics came out of wave optics.
I believe that any system that can be described in terms of a simple harmonic oscillator (which is the description of the vacuum in the Standard Model), can also be described in terms of coherent states like this. (See here for some examples: http://en.wikipedia.org/wiki/Coherent_state#Coherent_states_of_Bose.E2.80.93Einstein_condensates). I'm not an expert in this kind of stuff, though.
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Thanks JP. When you speak of coherence with multiple photons, I assume this is the essence of the light from a laser where all are in phase to a high degree?? It seems a remarkable "coincidence" that the two ways of viewing the problem can yield the same results.
What about pions and gravitons?? Do pions produce tangible waves in the short range nuclear force field?
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Having now read through the wiki reference I see my understanding of coherence in laser light is a bit naive :-)
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Hi Graham
Photons are not particles but I believe are made up from a minute volume of magnoflux. To make 3D EM radiation we must have an area of current[Ix*Iy at right angles to a voltage Vz] field. This is a new concept which has yet to be fully understood
CliveS
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It is a whole lot deeper than I thought. This is a good reference:
http://en.wikipedia.org/wiki/Photons
with the section entitled: Wave–particle duality and uncertainty principles.
I don't understand your reference re orthogonal voltages and currents, Clive, though I get the idea from generating a radio wave. And I thought that photons could be considered as particles (or at least wave-particles). Are they considered in this theory to be something different with a different definition?
In the wiki article they say: "According to our present understanding, the electromagnetic field itself is produced by photons, which in turn result from a local gauge symmetry and the laws of quantum field theory". Not having studied QED very much, this could be difficult to understand easily.
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Graham - wttw - the magnoflux theory is not merely "not fully understood". It's Clive's pet theory which has done the rounds of the physics boards without universal acclaim. A search on "An electric universe: magnoflux aether tunnel" might bring up a site with a pdf copy of this paper that gives a brief description. Personally, I distrust (and I realise this is a failing of mine) any scientific paper that describes a universe that God made.
I will not bother attempting to describe the theories this paper propounds as they are so far from the physics I have learnt as to be unintelligible.
Matthew
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I have wondered for a long time why the wavefunction associated with a photon is a tangible and measurable change in an electromagnetic field whereas (all?) other particles have a less tangible probability amplitude associated with them.
The photon wavefunction isn't quite the sinusoidal electromagnetic field variation, but the latter is very real and very detectable:
(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Fupload.wikimedia.org%2Fwikipedia%2Fcommons%2Fthumb%2Fa%2Fa1%2FLight-wave.svg%2F360px-Light-wave.svg.png&hash=2ad4863a372ec8afe556772a468ccd58)
Imagine a photon is travelling from A to B. You can measure this sinusoidal field variation at some point along the path. Now step away from the path, and measure it again. You will still measure a field variation, but it will be less intense. Step further away and it's even less intense. Integrate over a volume and say to yourself that the photon is a "pulse" of electromagnetic field variation, and you perhaps get a sense of "many paths". The photon, which might have a wavelength of say 1500m, does not exist as a billiard particle at any point location, instead it's a wave function distributed through space. It is however emitted or absorbed as a unit, so it can look very small. I don't see anything remarkable about this, after all i can shake the whole of a rubber mat using only my hand.
An example is an electron which exhibits interference and diffraction but for which the wave function appears as just an abstract probability amplitude.
IMHO the best way to conceptualize an electron is as a photon that is "wrapped" via pair production into a tight twisted circular path, something like a moebius strip. Now instead of being a transient passing field variation, it's a permanent standing field. The electromagnetic field is thus a part of what the electron is, and part of its wavefunction. You might say that the centre of this is at some given location, but again you can't say that the electron is a point particle at that location emanating a field. The electron itself is a "quantum field". Unfortunately IMHO some educational material depict it as something very small and pointlike, much smaller even than its Compton wavelength.
(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Fcasswww.ucsd.edu%2Fpublic%2Ftutorial%2Fimages%2Fphysics%2Fatom_struc.gif&hash=d932a71fe1501295ef12300780f708ab)
Are there any other particles for which the wavefunction is a sinusoidal change in a field?
Not to my knowledge.
If not, can any insight be drawn from this?
I think so, see Topological quantum field theory (http://en.wikipedia.org/wiki/Topological_quantum_field_theory) wherein the quantum field for say a photon has a different topology to that for an electron. It's related to knot theory, and in a nutshell advocates that the electron is essentially a 511 keV photon that's "tied in a knot". However TQFT doesn't seem too well-known these days, even though people like Witten and Atiyah have been involved in it. Some would argue that it isn't mainstream, but I think it will be.
If a Higgs Boson is found, would its associated wavefunction be tangible gravity waves?
No, because a gravitational wave is actually rather like a photon. I suppose you could call it a particle, particularly if you could keep pace with it and see it as a "bump" rather than just a wave. It's a particle in the same fashion as a single-photon electromagnetic wave, but the E=hf quantum aspect doesn't hold, so it's arguably less particle-like in nature.
As the photon mediates the em force, the graviton mediates the force of gravity and the pion the nuclear force (I think this is right but it is from memory), do these particles have tangible waves in their associated fields that produce identical results to a probability amplitude?
I'm afraid the graviton is speculative. It isn't part of the standard model. And whilst the gluon is said to mediate the strong force, we don't actually see free gluons, just as we don't see free quarks. So we can't talk about tangible waves like we can for photons.
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Are there any other particles for which the wavefunction is a sinusoidal change in a field?
But isn't the sinusoid nothing more than a way of describe the components of a generic wave? I'm not able to do the same with a generic field which allow for a wave description?
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Are there any other particles for which the wavefunction is a sinusoidal change in a field?
But isn't the sinusoid nothing more than a way of describe the components of a generic wave? I'm not able to do the same with a generic field which allow for a wave description?
That's true for a class of particles that satisfy the wave equation. I think the interesting thing about photons is that they don't individually look like sinusoids--it's that they tend to aggregate in collections that look sinusoidal.
However, if you look at a nonrelativistic electron traveling in empty space, for example, its wave function does look like a sinusoid.
That's a distinction between the way field theory treats particles and regular (Schrodinger) quantum mechanics.
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I found an interesting paper on the web:
http://www.google.co.uk/url?sa=t&source=web&cd=6&ved=0CDsQFjAF&url=http%3A%2F%2Farxiv.org%2Fpdf%2Fquant-ph%2F0604169&rct=j&q=photon%20wave%20function&ei=EIBhTKuBCc66OI3mza0H&usg=AFQjCNHL4hJrpj-HQhj6p5LJJJQyn_7arw
with a very long URL!!
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Very interesting, graham. Thanks. Here's a shorter link: http://arxiv.org/abs/quant-ph/0604169. I wasn’t too keen on When two photons are present, the joint wave function “lives” in a higher dimensional space, but it’s still very interesting indeed. I see it mentions On Physical Lines of Force. Take a look at that on wikipedia, in particular wiki page 53 (http://en.wikipedia.org/w/index.php?title=File%3AOn_Physical_Lines_of_Force.pdf&page=53). See where Maxwell mentions a screw mechanism? He's talking about the electromagnetic field in terms of “twist and turn”. The electric aspect is like twisted space, but if you move through this space you see the magnetic aspect, which is all to do with curl or rot, which is short for rotor. Or in other words "turn". The sinusoidal electromagnetic waveform is essentially telling you how much the space has been deformed by the displacement current. It's telling you the slope of a pulse, which is something like the “distortion” of a gravitational wave, see LIGO (http://www.ligo-la.caltech.edu/LLO/overviewsci.htm). Amazing stuff. IMHO what's even more amazing is that nobody seems to know about Maxwell's screw mechanism, even though it's restated as a "wrench analogy" two pages from the back of Minkowski's space and time. And take a look at the title of Maxwell's paper. It's "the theory of molecular vortices". He drew them as being in the space rather than the particle, which I find a little puzzling, especially since Kelvin had previously talked about atoms as knots and vortices. See A Circular History of Knot Theory (http://www.math.buffalo.edu/~menasco/Knottheory.html) for a bit on this.
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I didn't grasp the meaning of the 6 spatial dimensions but I took it to be a way of representing the wave function of two quantum-entangled photons occupying the same physical space; splitting the x,y,z components into 2 independent sets of axes maybe a way of doing it. I have not the time to follow up the references.
Yes, I know of the impressive "big science" LIGO project. It would be sad if it didn't find gravitational waves after all that effort even though that would also be an important result.
Didn't Maxwell write well? It is not over-verbose but is very clear; I think many people today would benefit from reading such work. Seeing this, I would like to have read his book when I was learning electromagnetic theory which seemed to jump from Flemings rules to the familiar vector equations.
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I didn't grasp the meaning of the 6 spatial dimensions but I took it to be a way of representing the wave function of two quantum-entangled photons occupying the same physical space; splitting the x,y,z components into 2 independent sets of axes maybe a way of doing it. I have not the time to follow up the references.
I agree--they're using two sets of position coordinates to describe a superposition of two states, which makes 6 independent position coordinates, or 6 dimensions to the space describing the system.
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graham: I have this concept of a photon as a 3D version of stretching a Flatlander's sheet whilst keeping it flat. There's no extra dimensions involved, just a "gauge change" displacement. Hence I struggle with 6 dimensions when describing entanglement. I think the issue for LIGO is that is they're trying to detect what is in essence a spatial distortion using light, which is in essence... a spatial distortion. So it could be they'll get a null result. Hence the interest in using clocks in the form of pulsars. See Pulsar watchers race for gravity waves (http://www.nature.com/news/2010/100112/full/463147a.html). Yes, Maxwell did write well. IMHO he's misunderstood and much overlooked, in that the Heaviside vector approach describes "what it does" not "what it is". But fingers crossed, that might change, new chapter and all that, see http://www.physorg.com/news182957628.html. In PhysicsWorld next month there's going to be a "Not so loopy" article about knot theory and "smoke rings produced by a machine in 1867". Speaking of which, did you see my little article in PhysicsWorld last month? Mr Newton's Classroom. Only a bit of fun, but one guy even said he was going to reference it in a paper. I'll believe that when I see it!