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Post by carnyx on Mar 17, 2011 0:30:17 GMT 1
Ellipses have two focal points, except when they are circles. And viewing them obliquely, they can be seen as circles .. and also lines.
A satellite's orbit can be elliptical, with the Earth at one focus. But what is at the other focus? A 'virtual' Earth?
And if we consider EM waves, could they be elliptically rather that circularly generated? And if they are, could there also be some displacement along the axis of propagation?
And if so, how could this cyclic variation in speed be detectable?
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Post by Progenitor A on Mar 17, 2011 10:30:00 GMT 1
Can't answer your other questions but elliptically polarised em waves are possible
The same principle as the Lissajou figure - remember that from your apprenticeship days?
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Post by carnyx on Mar 17, 2011 11:08:28 GMT 1
Ah Yes!
And thanks for the comment on elliptical polarisation, which somebody must have explored as a possible source of insight into the two-slit experiment.
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Post by speakertoanimals on Mar 17, 2011 17:40:25 GMT 1
Except you're not taking a wide enough view. Orbits can be either closed (circles, ellipses), or open (parabola, hyperbola). All conic sections.
DO you mean polarised, or do you mean elliptical (rather than spherical) wavefronts?
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Post by carnyx on Mar 17, 2011 17:50:52 GMT 1
@sta,
I mean elliptical, as opposed to sinusoidal, waveforms.
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Post by speakertoanimals on Mar 17, 2011 20:46:23 GMT 1
So do you mean you want am em wave propogating not just as a simple sine wave -- because elliptical waveform doesn't make SENSE? How can a wave be an ellipse? It can be square, or somewhere in between, but it can't be an ellipse since what the wave means is the Value at a point in time, and across space. AN ellipse would mean having TWO values at the same point at the same time, which makes no sense, since the field at a point has ONE value at an instant, not two.
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Post by carnyx on Mar 18, 2011 9:18:02 GMT 1
I am merely speculating, as a recreational exercise, so I woud appreciate you keeping your asperities to a minimum (unless of course they are amusing)
As a very narrow example, one can see elliptical movement in particles in the phenomenon of 'Stokes drift' .. despite the apparenly pure sinusoidal motion of the mass
But what is the problem of apparently having two values at the same point? I mean, ellipses do physically exist, as I pointed out in my OP
And in the case of EM waves, if there is an assymmetry in the ratio of permittivity and permeability in the medium, them we will see a polarisation ... which is an elliptical phenomenon, no?
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Post by Progenitor A on Mar 18, 2011 9:39:51 GMT 1
Carnyx
Just as a sinusoid is generated by a a point moving around the perimeter of a circle, where the instantaneous amplitude = sin0, where 0 is the the moving point point on the circle makes with respect to the +ve x axis, there is absolutely no reason why another waveform cannot be generated by an ellipse eith a point moving around its perimeter.
Don't know what the mathematical function for the instantaneous amplitude will be off hand!
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Post by speakertoanimals on Mar 18, 2011 15:23:25 GMT 1
Because it doesn't make sense! Look at electric field -- it is a vector, with magnitude and direction. What does it mean? Well, magnetic effects aside, it is the size and direction of the force an electric field would exert on a test particle at that point at that instant.
Hence by definition, can only have ONE value.
The combination of a vertical electric field and a horizontal electric field at the same point isn't TWO values, but the single value that is an electric field inclined at some angle to the horizontal -- but a single field. a single value, not two values. Two components, yes, but the test particle gets pushed in ONE direction.
Ditto magnetic field. And ditto other physical variables which have scalar rather than vector values. One point, one instant, one value.
Do you mean asymmetry in space, or asymmetry in terms of the direction of propogation of the wave, or asymmetry in terms of polarisation of the wave? So you can have substances where horizontally and vertically polarised waves move at different speeds (such as birefringent calcite crystals).
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Post by Progenitor A on Mar 18, 2011 18:51:30 GMT 1
But what is the problem of apparently having two values at the same point? I mean, ellipses do physically exist, as I pointed out in my OP Take no notice of the background noise, Carnyx. An ellipse does not have two values at one point; all pointa are spatially separated and if we traverse an ellipse, are separated in space and time. |
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Post by eamonnshute on Mar 18, 2011 19:19:41 GMT 1
Waves on water have a sinusoidal shape, but what on Earth would they look like if they had an elliptical shape? A sine wave (y= sin x) has only one value of y for any value of x, but an ellipse (ax^2 + by^2 = 1) has either two values or none for any value of x. That is why an elliptical wave does not make sense - the height of the wave can only have one value at any point.
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Post by Progenitor A on Mar 18, 2011 20:59:02 GMT 1
Are you suggesting that a waveform cannot be generated by traversing the perimeter of an ellipse and tracing the instantaneous value against the angle made wrt the x axis, in exactly the same way as a sinusoid is generated using a circle?
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Post by carnyx on Mar 18, 2011 21:12:56 GMT 1
@sta
As I said;
This means a variation in the ratio between the electrical and magnetic 'conductivity' in the medium, over a distance, will cause a varying polarisation of the wave .... which will make it elliptical.
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Post by eamonnshute on Mar 18, 2011 22:47:55 GMT 1
Are you suggesting that a waveform cannot be generated by traversing the perimeter of an ellipse and tracing the instantaneous value against the angle made wrt the x axis, in exactly the same way as a sinusoid is generated using a circle? If light travels along the x-axis, and we plot the electric field in the y-z plane at one point then we get an ellipse (with a circle or straight line as special cases). However, along the x-axis the field at any instant is sinusoidal. I think this is what the confusion is about. |
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Post by speakertoanimals on Mar 21, 2011 12:58:51 GMT 1
If we traverse a circle at constant speed, we do indeed get a sinusoid as the x or y component of the motion.
If we do the same for an ellipse, the first point is WHAT speed is constant? If we use the parametric equation for an ellipse, we get:
x = acos theta, y = b sin theta
So if angular speed is constant, theta = omega t, we still get a sinusoid.
If we project onto some direction other than the major and minor axes (x and y axes in this case), then we just get a combination of cos theta and sin theta, which is STILL just a sinusoid, albeit with the phase shifted.
So what remains? We could try and traverse an ellipse at constant linear speed (which isn't what planets do BTW), but which will probably involve some messy maths with elliptic integrals............
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