The answer is no: not all white noise sounds alike!
White noise can sound like "hissing" of a shortwave radio or it can sound like a Geiger counter (click..... clickclick............ click).
More:
A noise process is "white" if every frequency has the same power spectral density.
Any process where any two samples taken at different times will be statistically independent is white in this sense. In other words, if knowing the amplitude of the noise at time x tells us nothing about the amplitude at any other time, then the noise must be "white."
But there are many different-sounding processes that have this characteristic, because just knowing that two samples are independent does not tell us the distribution of the individual samples.
- One classical example is "thermal" noise, in which the samples are distributed according to a normal, or Gaussian, distribution. This is known as "white gaussian noise," and typically in communications will have been added to the signal we are interested in: hence, Additive White Gaussian Noise (AWGN). This sounds like "hissing."
- Another kind of white noise is "shot" noise, which can come from any Poisson process, including the particle decays heard by a Geiger counter. Here the individual samples aren't Gaussian deviates; they are impulses, either zero or big, and most of the time they're zero. But since knowing the time of one "click" tells us nothing about any other (and because each click carries all the frequencies), this is also white noise.
The answer is yes -- if you mix light from a laser (monochromatic light) at 700 nm with another laser at 400 nm, the resulting radiation will be different from any monochromatic light.
That's true in two ways:
- The resulting radiation is radiometrically (or physically) distinct from any monochromatic light. Adding two sine waves of different frequencies won't make a sine wave.
- The resulting radiation is photometrically (or perceptually) distinct from any monochromatic light, when observed by a human with normal (trichromatic) vision.
You can see this on the CIE standard observer colorimetry diagram:
(from http://en.wikipedia.org/wiki/CIE_1931_color_space)
This horseshoe-shaped figure represents the human perception of color near the area of focus (where cones predominate), once overall brightness (luminance) is factored out.
The top outside of the horseshoe (with the numbers going from "380" on the lower left to "700" on the lower right) is known as the "spectral locus": it represent the colors you can get with monochromatic light, e.g. by varyting a laser in wavelength from 380 nanometers to 700 nanometers.
The bottom line that directly connects "380" and "700" is known as the line of purples. These colors (all shades of purple) cannot be made by any single laser! And the entire interior of the horseshoe, including the middle where "white" is, also requires more than one laser.
Your color -- a combination of light at 400 nm and 700 nm -- will be found somewhere very close to the line of purples. (The more 400 nm, the more it will be closer to that side, and vice versa.) You can tell from the diagram that these colors aren't on the spectral locus, and therefore can't be made with a single laser.
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The standard "R'G'B'" color spaces work by picking three illuminants from the inside of this diagram. (These can be three phosphors on a CRT, three filters on an LCD, three slices on the color wheel of a DLP display, three layers of emulsion on a piece of color film, etc.) Each illuminant's color has a point within the horseshoe, and the three points form a triangle. By varying the amount of R, G, and B, we can make a color that is perceived the same as any color that lies within the triangle.
Here's one of the most popular triangles, known as the ITU-R Rec. BT.709 or sRGB primaries. The three colors on your computer monitor are probably close to these points on the triangle, meaning your monitor can make any color within the triangle. But as you can see, it takes three illuminants to have any nonzero area in this "perceptual" space of colors (again, with luminance already factored out).
No single laser can do it.
There are some big differences between living in a plane, versus living in Euclidean 3D and merely being able to perceive only a plane slice. Here's one: the wave equation in three dimensions is "nondispersive," meaning all frequencies travel at the same speed and the region of influence of an impulse is just an expanding circle. So if you say something 100 meters away, or transmit a signal from your radio, I will hear a delayed, quieter version of what you said.
In two dimensions (or any even number of dimensions), the wave equation is dispersive! You do not just hear a delayed, quieter version of stimuli at a distance; the sound itself is actually changed by traveling through the medium. The region of influence isn't a circle; it's a filled-in circle. Imagine throwing a rock into a pond -- the resulting ripples aren't just at the outside of the circle. The rock continues influencing the interior of the circle even after the first news of its plop has passed by. Similarly, the sound of thunder, constrained to a near-2D slice of the earth's atmosphere, is not just a bang when you hear it from far away. It gets transformed into a rolling sound because the different frequencies travel at different speeds.
So a flatlander who understood partial differential equations (this may be a small number of them...) could distinguish between these two possibilities (2d world, versus 2d slice of 3d world) by observing the behavior of waves as they propagate.
(NB: The proof that the wave equation is dispersive in even-dimensional Euclidean spaces and nondispersive in odd-dimensional spaces is really frickin' hard! I have seen it in a monograph and did not understand it at all.)
