At lower frequencies, there's no reason to think that an infinite number of frequencies may be attainable. After all, if you move a coil winding a smidgen of an atom one way or the other it will affect the resonant frequency. Same with a cavity.

But, when you get above the frequencies that can be achieved by such "mechanical" means, are there frequencies that simply cannot be achieved at all? Is there a mechanism, within our physical universe, that can prevent them?

Let's zero in on the visible spectrum where we can think of colors as colors. If colors are generated by the interchange of energy between electrons and photons as the electrons jump from orbit to orbit, in a quantum world are there energy gaps that simply cannot exist and thus are incapable of producing some frequenies of light (or perhaps most frequenies of light)?

If there are only about 100 elements and a finite number of orbital energies, it would seem so. However, not all light (even light that seems like maybe it should be) is monochromatic. A red LED does produce red light but, only when the light is trapped in a mode that favors the "real" frequency, as in an LED laser, does it come out monochromatic.

So, I guess the question may be whether there's enough of that "tolerance" across the elements and all their possible orbits to produce a truly continuous spectrum or are there still gaps for which a color cannot be generated; an "illegal" color?

I wonder if anyone has writeen a program that takes into accouint all the possible energy levels for all the orbits of the electrons of all the elements and includes the tolerance allowed for each and plots a spectrum that would show if there are indeed those "illegal" colors.

Does anyone here have a sense of this? I had touched on this earlier but, decided to "formalize" it with a thread.

 

Disclaimer: I am not a physicist, as any physicist reading the following will tell you.

I'd suspect that in one way, yes, you could say that there are illegal colours. If the Planck length exists then there are a limited (although still unimaginably vast) number of positions electrons could occupy, and therefore a limited (though even more vast) number of jump lengths/energies they could make, so the number of possible wavelengths could be limited (although insanely, mind-buggeringly huge).

I don't think we will see the computing power required to count it up in my lifetime or my son's. Perhaps someone could prove it mathematically, but I couldn't even begin to describe an experiment to explore it.


Torben

 

Interesting question. I would guess black and white would be illegal colours as these don't exist outside of our minds. Don't astronomers work out the constituent parts of objects from the spectral bands they emit. The sun's spectrum has lots of dark bands throughout it and I think it contains most elements. So, my guess is yes, there are unobtainable colours but we may be able to see some of them.

Mike.

 

Good answer, but remember there are also vibrational levels within each electronic transition. That of course, increases the number of potential "colors." John

Edit: Of course, I am referring to molecules, not individual atoms. Also, with molecules, different arrangements and different elements give even more "colors."

 

In astronomy stars moving away from us show a red shift. These shifted colors may not be possible by exciting atoms or molecules.

Take three filters Red, Green, and Blue. Place them in front of clear tungsten bulbs. Control the light intensity with rheostats to mix the output from the three bulbs to make a continuous range of colors, within the limits of the bulb/filter setup.

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I had thought of the red shift aspect and it does seem like, even if a color is "illegal" it may be synthesized by doppler shift.

Also, the rheostat comment raises another, perhaps profound question. If the slightest change of a rheostat changes the color of an incandescant bulb, how does that change relate to the physics of it all? Certainly, elemental tungsten has electron energies and if vaporized will emit (and absorb) spectral lines but, if it's temperature is changed just slightly to change the color does that even relate to the energies of the elctron orbits of the element?

Did I ask a meaningless question by assuming that all phonton wavelengths require the interchange of energy between the electrons and photons?

 

Incandescent bulbs emit a mixture of wavelengths.

That is why we can filter out a color (actually a range of color) with a gel/filter. Changing the rheostat will change what the bulb generates but since the filter is a band pass sort of affair only the color(s) we are interested in make it through the filter.

We may be mixing apples and oranges.

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OK, I'm thinking about this slightly differently now. Supposing that the universe is finite, and also supposing that the number of photons in the universe is finite, then given that any photon may only have one energy at a time, the number of simultaneously occurring colours in the universe must also be finite.

However, perhaps individual photons can "slide" into different wavelengths (i.e. via Doppler shifting), changing *which* set of colours is actually represented by the photons in the universe.

Something like this: while a computer monitor may be capable of reproducing 16.7 million-odd different colours, it cannot reproduce all of those colours at once since the monitor does not have 16.7 million pixels with which to represent them (not a perfect analogy, but hey).


Torben

 

While it is true that electron energy in bound states is quantized, dropping from a higher energy level to a lower energy level is not the only mechanism of photon production. Remember back to the golden days of yesteryear when a hot filament would change colors as it warmed up. Certainly blackbody radiation is capable of producing a color continuum since it depends on a different mechanism for producing photons.

See the following article for color as a continuous function of temperature.

http://en.wikipedia.org/wiki/Black_body

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I see two different definitions of color being used here, and I think some people are confused.

There's the energy of a single photon (and by extension, any number of photons with the same energy). Many people associate this with color. It will activate the sensors in our eyes according to which sensors are relatively sensitive to that wavelength.

Then there's the mix of different wavelengths that we see every day. We see these as color as well, because our sensors are stimulated by the various wavelengths present, in proportion to how each present wavelength overlaps the sensitivity curves.

 

I'm not sure what others talk about but I'm keeping it "simple" (ha ha) and just thinking about the energies. If we get into the perception of mixed colours then the number of possible combinations just gets silly--if it wasn't already.


Torben

 

Well, just to throw another monkey wrench into the mix, here's something that "amplifies" the importance of doppler shift in the color question.

http://www.colorado.edu/UCB/Academic...bec/index.html

I found this to be an extremely interesting read...perhaps largely because it's presented on "my" level. It's a whole little tutorial on the Bose/Einstein condensate. Pay special attention to the notion of using lasers to cool the matter and the importance of the doppler shift associated with their motion.

Also, the Wikipedia link earlier does reaffirm the quantum nature of "colors" (more generally electromagnetic radiation). So, the question still remains whether there are "illegal" colors. As a related point, if you have two pieces of mesh material in which the meshes have some integral relationship (pieces of screen door screen, fabric, cyclone fencing, etc.) and you look through them and get an interference pattern, do you really have "new" frequencies? Certainly, in radio, as you heterodyne signals they are treated as new and real. Same with doppler shifted things.

 

If you are not going to talk about color perception then you should not talk about color. Color is perceived.

So maybe there are "Illegal Energies" but not "Illegal Colors".

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My initial post on this topic specified that we should limit the spectrum to the visible spectrum for exactly that reason. So, the term "colors" would have meaning. I also avoided the mixing of colors because those are perceived colors rather than colors of specific, measurable wavelengths.

For reasons given in my last post (just before the one before this one) I'm not sure that mixtures of colors are "real".

But, to respond to your point: Are there illegal energies, which then cannot be imparted to photons to represent certain colors (even within the visible spectrum)?

 

Did I not already answer that question? Changes in the quantized energy levels of bound electrons is NOT the only method of producing photons. That fact has nothing whatsoever to do with perception.

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