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I have a 'thought experiment' which I'd like to ask about.

I was thinking what speed I would have to drive towards a crossing to see a red light as a green light - pretty easy, using the doppler effect for electromagnetic waves. I'd have to be driving around $1/4\times c$. Now I started wondering... how would I see something purple?

Like what if there would be a purple (smallest visible wavelength) ball next to the street, the wavelength would shift out of the visible light spectrum for me so would I just NOT see the ball? Or does it also radiate other wavelengths which would shift into the visible light spectrum?

Assuming it doesn't, would I just not see the ball?

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Yup, you would probably still see a color because the previously invisible wavelengths that were either too high or too low to be visible would Doppler shift to the visible light interval. Otherwise I recommend you a highly realistic PC game A slower speed of light, see more comments at… – Luboš Motl Feb 5 '13 at 17:26
But note that the ultraviolet portion of the sunlight is shielded by the atmosphere so it wouldn't hit the objects and couldn't be reflected. So if you were traveling away from the objects, so that you expect red shift, the original light that could become visible after the Doppler shift would be originally UV, but almost no UV light is reflected from the object because no UV light makes it through the atmosphere, so the object would be rather dark, indeed. Similar considerations apply for the red shift - moving against the object - and the atmosphere's effect on IR light. – Luboš Motl Feb 5 '13 at 17:28
Under appropriate artificial light, e.g. (thermal) light from the light bulb, almost all frequencies are represented, including those higher and lower than the visible interval, so the object would never look dark under a moderate red shift. I have to emphasize that the effect of the Doppler shift both on the incoming light's frequency as well as the frequencies that the object is able to reflect have to be considered to get the final color. – Luboš Motl Feb 5 '13 at 17:32
I originally wrote that the object would look black. I realized this wasn't correct for the reason Lubos pointed out in his last post, namely that what you would see would crucially depend on the reflectance spectrum of the object – joshphysics Feb 5 '13 at 17:37
@LubošMotl you should make your response an answer – DilithiumMatrix Feb 5 '13 at 18:02

Yes, you won't see the purple light because it's in the UV to Xray, depending on the actual speed and the angle you are looking at (sideways there'd be no change, if you go straight, and you better go straight).

Behind you there would be red-shift.

If you go fast enough, the 4 K background radiation (residue of the big bang, normally micro-wave wavelengths) would become visible, so that would be get pretty bright upfront.

See this article

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Sorry if I am reviving an old topic, but isn't purple technically how we perceive a combination of red and blue, and not actually a pure wavelength in itself? I'm pretty sure the original question uses 'purple' to refer to violet (i.e. the wavelength after blue), but this makes the question a lot more interesting: say the object is purple, so it gives off both red and blue wavelengths. Let's just ignore how reflection works, and just say it's some particle that somehow emits red AND blue wavelengths. Then, whichever way it's travelling relative to you, whether it's coming or going, either one of those wavelengths is going to get bumped into the invisible spectrum, and the other wavelength becomes progressively greener...

So you'll get something like purple -> blue -> green -> red or purple -> red -> green -> blue depending on which way it's going.

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Well i guess that if we are able to travel at speeds approaching the speed of light invisible things can become visible and visible things can become invisible,therefore you will not see your purple ball.

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