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I want to ask if the human eye can see only photons particles between ultra violet and infrared wavelengths, can we see other particles (that have a wavelength between ultra violet and infrared) moving in the space available?

Are non-photon visible particles available in the earth's atmosphere?

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The receptors in the human eye are tuned, as you say, to photons of wavelength higher than infrared and less than ultraviolet. The signal of sight comes from such photons which are absorbed by the receptor cells.

Even if the de Broglie wavelength of a particle were within the receptor wavelengths of photons, the receptors are tuned for photons only, so a particle cannot excite them to send a visual signal.

There exist particles continually flowing through the atmosphere,of all energies, the cosmic rays. Most of these are muons which may interact with the electromagnetic fields of our eye non destructively, since they have no strong interactions. In this interaction there may be photons emitted in the appropriate for sight range. The passage will be very fast and it is doubtful that the brain will register it as an event.

Astronauts who are exposed to cosmic rays not filtered through the atmosphere, which might interact strongly in their eye, might observe sparks/flashes-of-light from the interaction, because there would be many secondary ionizing particles from the interaction.

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+1 and see for more about the cosmic rays. – John Rennie Sep 24 '12 at 6:28

Yes, a finger in your eye will stimulate photoreceptors. I don't (entirely) mean to be facetious. You can get those cells to fire lots of different ways including mechanical energy--this is why people with retinal detachments see "lightning bolts" in their vision.

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