Transverse Electromagnetic WavesPoints27 - 10 Answers
[Furuici], I curious to know how the visualization of anything (with the exception of the theoretical realm i.e. Superstring theory - or maybe spacetime deformations?) would require a five-dimensional image! Let's say I assume one is time, that's still four dimensions roughly one more spacial dimension than there was the last time I checked! Are you representing something that's not actually a dimension as being a dimension? I may be misunderstood something, but I would expect if it can exist in three spacial and 1 temporal dimension, I could visualize it the same or less dimensions. I'm just curious what your talking about, that's all.
Points27 I think I can tackle this one! But my only question would really be,...could someone please answer Points27 previous question? It's the only part I cant resolve I don?t know what orientation the waves would or could occupy relative to the others. In other words If I visualize a wavefront that is emitted from a single point or spherical source, I would similarly expect that to be the shape of the leading edge in space as it grows in size over time, or a solid "3+1" dimensional spacetime sphere that varies in consistency according to it's movement pattern. But I am at a loss as to what the alignment pattern of the adjacent waves on the sphere would be. What would the conditions present at the time of an emission like this predict the pattern to be?
My attempts to match a spherical wave(s) with individual rays at given points should match up if it it's correctly arranged. The component waves that e derive from a spherical wave should match up perfectly, but I can't think of an arrangement that this will work for. I considered several patterns, some trivially and others trying to design one without seams, overlaps, or points that don't fit the pattern ideally for a given ray. I can't imaging the "ideal pattern", there's always a minor glitch at some point! I cant imagine a design that doesn?t have at the least endpoints on either pole that would cause interference. I don't expect that such a seem would exist in the real case. I tried aligning the waves like longitude and latitude lines on a globe. If I slice it into cross-sections (mentally) and align the rays that match the waves to encircle each circumference so that the last one matches the first and all are facing the same direction, the sphere has smaller and smaller clockwise circles until the two pole where I would have to choose a completely random direction for it which would interfere with some of the surrounding circle. Sounds unnatural!
I?ve tried splitting the sphere medially into equal haves and make one ring of aligned wave fronts, then reassembled and repeated with all further cuts starting on the left and passing the previous one in the center axis then exiting the back to the right of the previous slice, so it's like if you spin a ring, filmed it, and stacked each frame they all over lap, line up and the end point mystery goes away. It's replaced by a new endpoint issue, each "great circle" that was made crosses at the poles, so there are multiple, many or possibly infinite differently facing EMR rays at each pole!
A torus eliminates endpoints/poles, and is a very tight one was used it would be almost a perfect sphere, but I don't believe that the source would have generated such a shape. Plus there?s waves emitted from the inner surface too. So that's a no go!)
I can clearly visualize the motion pattern with these but their not "right" so why describe a random creation? There must be some pattern that will allow a flawless spherical shape to be produced.
And as far as your question about if there are infantile wave functions that make up the EMR emission, it seems to be the case when you see the merged sphere, and imaging it's endless expansion from a central point, but first, unless the rays have no energy (obviously not) that it would require infinite energy to make any pulse! Secondly, if there was infinite electromagnetic waves, the strength of the sphere would constantly rise as it sped across space at the speed of light growing exponentially and all such waves and even visible photons would fill the sky with all the light to any minor light that there ever was in the universe (when it reaches us of curse), but the night sky would be pure white. Therefore, they necessarily must be finite - this can be seen as the strength of the signal diminishes with time proportional to the "surface to volume ratios", of the sphere representing the wavefront. Thus limiting it's meaningful distance before it is considered negligible.
The energy must be quantized, and overall it's conserved , that is the energy is conserved. so it grows diffuse very quickly as it propagates through space! But then it remains "continuous" the individual rays that we general speak in the language of for simplicity (and arguably, for confusing people!) never diverge leaving gaps or individual rays to bifurcate from one another!, A wave, therefore, at least of this type and dimensionality is a specific type of wave-entity that is a sphere in 3D space that propagates by appearing to inflate. It's obviously possible to have oscillating groups of waves following one another and providing measurements like wavelength to be found by the separation distance of concentric spheres you would find similarly inflating inside the outer wavefront. The waves would have faded edges since they are not square-waves of course! Your lake medium example would show circular 2D waves that oscillate in 3D space over time, but people will call it a 2D (plus time - sometimes this detail is omitted) wave. I realize the wave motion and usefulness uses a two dimensional plane, but it's rippled. The way I see it, three dimensions are needed to produce the waves, if there were but two spacial dimensions, I would need to either be 2D and only possibly notice some odd measurements in space at the time, or watch a 2D plane oscillate from the three dimensional universe I'm in now. But, without thickness I would never be aware of the wave or the plain! So shat why I don?t think of the EMR animated GIF posted above by another user is a one-dimensional wave It's not even two, but three-dimensions plus time are necessary for that wave to occur at the bare minimum, or else I guess it just drops dead!
In 4D spacetime a pulse would generate a SOLID sphere, even though there was but a single pulse, since each moment of wave movement is present simultaneously if you moved a time-muscle you could see the various thicknesses right down to the "first" , if we discover the pattern then I can explain what you might see next to the previous moment to observe the very interesting diagonal twisting and turning over the surface of the sphere as we examine it at various times positions. If to wave crests occurred, the sphere would be solid just like before, but if we dissected it or just stepped to the past a few nanometers, each moment in time of the dual wave's propagation is , there , clearly recorded for each moment of time!
I consider it much more boring, but I could explain it in he common "2D space x 1D time" spacetime, but this is going to be the type that has world lines and "light cone", motion transformations involve curvatures to accelerate, and so forth. It's clearly unnatural and while it has it's uses, it won't give a real idea of how the wavefront would appear!
But no matter how you slice it, I have to know the manner with which the electromagnetic wave would emerge from the source to describe the behavior it displays, Isn't that able to be inferred from the type of source or figured out somehow? I tried using just the vector sum and sought an arrangement that had symmetry and no vectors out of place, I tried a S repeating pattern, - I just cant figure out what is or at least sees like it may be produced from a point emission, give me that and I believe I can explain it's appearance. From the ones I tried , The behavior I could visualize was pretty peculiar.
Anyway, lemme know...
If the entire 3D sphere wavefront, that is "impossible to see literally, only interact with, of course" oscillates as a single unit as it enlarges - let's say "up and to the left", and then back then "down and to the right", the upper-right to lower-left central axis that it would have to be rotating on (at least a few degrees for each cycle) would be moving in a completely different way ( much smaller circular oscillations at the axis area. So what I'm saying is a circle doesn't appear to simply be translatable to a sphere like you mention. Do you see what I'm saying? Unless the rays are acting independent of the spherical shaped waves (meaning there is no coherent sphere shape any more). Unless you can describe what your thinking a little bit more thoroughly, I don't believe that a circle "going out as a sphere" describes a transformation that oscillates as a 3D unit.
3-D visualization is very hard. However, in 2-D you can get a start. Picture a drum head instead of a string. We you hit it you generate a two dimensional wave across the head. That's fairly easy to see.
The other thing to consider is that although the EM wave is transverse, the direction in which it propagates is perpendicular to the transverse directions. So if you can visualize a two dimensional ripple, why not visualize a three dimensional one going out as a sphere.
A final thought, the source we are considering radiates individual photons in all different directions. However, there are so many being emitted at one time that we can see radiation in all directions all the time.
A good way to visualize the action of 3d waves is to think of them as pulses rather than waves. Imagine a globe getting bigger, it will expand in size in every direction. Now imagine this expansion is like a layer leaving the globe and getting bigger and bigger. Then another layer leaves the globe inside the first layer. Think of the thinkness and the speed of the layers leaving as different wave frequencies and lengths. A layer would be densest in the middle, corresponding with the peak of the wave, gradually getting less dense to a point in between layers which would correspond to a wave trough.
I am not so good at explaining things, I hope this makes sense.
Electromagnetic waves consist of two transverse waves, the electric wave and the magnetic one, travelling perpendicular to each other. The direction of propagation of energy due to electric and magnetic vibrations is perpendicular to the movement of both the waves.
Both of these waves are considered transverse because the electric and magnetic fields (analogous to
'particles' in a transverse wave) move up and down and right and left respectively. while the wave itself travels perpendicular to both.
(3D diagram of an electromagnetic wave from Wikipedia)
A spherical wave front can be made over a point sources emitting electromagnetic waves in all directions. Electromagnetic waves can then be viewed as rays being emitted from that point source in all directions. These rays consist of electric and magnetic fields travelling perpendicular to each other/ Both of them are transverse in nature, which means that the electric as well as magnetic fields are vibrating to and fro perpendicular to the radius of the spherical wave front with a certain amplitude. Further, they tend to hit the surface of the spherical wave front in one phase....
I understand all that , but what I am trying to get at is how can all this be pictured on a spherical wavefront? Textbook / Wikipedia or whatever illustrations/animations always show a diagram of two orthogonal traveling waves, the electric and magnetic waves, as if the source is sending a ray out in one direction. For an omni-directional radiating source, how can this be visualized? Forget the fact that the wave is traveling outwards for a moment and pick an instant in time. On the spherical wavefront, what does the distribution of electric and magnetic fields look like?...
You can visualize a longitudinal wave in 3d as a density of a smoke, but you can't visualize in 3d a transverse wave. It would be a 4 or 5 dimensional "image". The textbooks can only give you a picture when the radiation is 1d, at this way the image is already a 3d image. ( I know its 2d in paper, but you visualize as a 3d image). So the main problem is when the radiation is 3d, the image bacome too complex , and more than 3D....
If a point source sends out rays in all directions, is there a finite number of rays with a specific angle between them? I thought the concept of "rays" was just a convenient way of thinking about radiation so that problems in geometric optics could be worked out?...