- Let´s talk only about photons absorbed by detector. Would it detect something else if the photons came from blue star than if the photons were filtered by blue paper?
- And what about ultraviolet paper?
No star emits a single frequency of radiation - they all emit a spectrum, and the wavelength of the light that's most intense in the spectrum depends on the temperature of the star.
The spectrum of the light transmitted through a blue paper depends on the transmittance of the paper for the different frequencies that make up white light.
In the off-chance that both spectra are identical, you could say both blues are identical.
The only properties a single photon has are its direction of propagation and its energy/frequency/wavelength. So a photon of a given wavelength coming from some direction is just that -- it doesn't carry extra information about what caused it to be coming from that direction with that particular wavelength.
Now there is a caveat that has to do with interpreting the wording of your question. If by "blue" you mean "wavelength of 450 nanometers," then the above is all there is to say on the issue. Often in science we use "color" interchangeably with "wavelength."
However, if by "color" you mean "as seen by the human eye," then there is likely some difference. In practice, any source of light, whether it be a star or an illuminated piece of paper, has a detailed spectrum -- a distribution of how much light is at each wavelength. This is what you see when you break up light with a prism or a diffraction grating.
These spectra will in general be different for different sources, since all sorts of things can affect them. For example, gasses in a star's atmosphere absorb very specific wavelengths, preventing these from reaching you. The molecular bonds in the paper will absorb different wavelengths.
Now because the eye only has three color receptors, and all of these sensitive to a broad range of wavelengths, fine details in spectra are lost to us. There are many different spectra that will produce the same levels of stimulation in these receptors and thus be seen as identical colors. In this sense there are different "blues" and we would need a spectrograph rather than our eyes (or even regular cameras, which are similar to our eyes in this regard) to detect the difference.
Since UV is just slightly shorter wavelengths than visible light, all of the same discussion holds there.
- Yes, probably. There are a lot of ways that your eyes/brain can see "blue" with different mixtures of light. A star, paper, and an LED will all have different combinations based on the way they make that color, but it can still look the same to you. A spectrometer, which can analyze the actual mixture of frequencies entering it, will be able to distinguish from these. A camera may or may not see them differently, since a camera works more like your eye, but with different ways of measuring the mixture of light.
- Yes, for the same reasons, except that your eye wouldn't really know what to make of ultraviolet paper. I suppose it would just be black.
This question is partly a biology question, because color, blue in this case, is labeled by human perception of what blue is.
As far as physics is concerned, photons make up light and photons come in all frequencies of the electromagnetic spectrum. That spectrum, the optical part known as rainbow.
The biological perception by the receptors in our eyes retina sees and registers the blue of the spectrum as blue, i.e. the photons/light of wavelength 450-495 nanometers. But our perception is very much more inclusive, and can have combinations of other frequencies raising the perception "blue" without the frequency blues being there.
Edwin H.Land , the inventor of Polaroid cameras, showed that one could get a perceived full color picture by just using two frequencies for illumination.
The blue light coming from the stars through the mostly void has the frequency of blue. The blue of a blue paper might have it or might not , or the photons coming through might have a mixture of frequencies that raise the perception "blue" in the brain.
Just two frequencies could do it, as was shown in the demonstration. There is blue where there is no frequency blue .