Double Slit Question

[Ziggurat]

No, a photon of light can only have one wavelength. This can be known.

Not in general. A photon will only have one wavelength if it's in an energy eigenstate. Which you can get for a photon in a standing wave, but which you cannot have for a propagating photon.

The Uncertainty principle says

You have missed the relevance of the uncertainty principle in relation to light. Wavelength and momentum are related. How do you get uncertainty in momentum without having uncertainty in wavelength? You cannot, unless it's a standing wave, which clearly isn't the case in a double slit experiment.

The Wikipedia description makes an implicit assumption (that the length of the photon, which is NOT the same as the wavelength, is longer than any path differences in the regions of interest) which I have made explicit. The length of the photon is the distance it's spread out over, which corresponds to the uncertainty in the position and which is inversely related to the minimum uncertainty in momentum (and hence wavelength) via the uncertainty principle. This length can be much longer than the wavelength, and must be if the wavelength is well-defined. Once you understand this, you will see that there is no contradiction between what I said and what Wikipedia said.

 

[Reality Check]

No, a photon of light can only have one wavelength. This can be known.

The Uncertainty principle says

The physical properties of a photon include that its momentum is inversely proportional to its wavelength. So a measurement of a photon's wavelength is the same as the measurement of its momentum. If you measure that a photon has an exact wavelength (i.e. momentum) then you lose knowledge of its position as the Uncertainty principle says.

 

[Ziggurat]

And is it possible to know the velocity and time taken from emmision to detection for any of those?

With what precision?

or is that where the fact that making measurements affects the conditions messes everything up?

All you need is for the momentum to be sufficiently well defined that you can treat the initial wave as being monochromatic. That requires some uncertainty on position, but that minimum position uncertainty is actually quite small from the point of view of an experimental apparatus. So you're never really operating against the limit of the uncertainty principle in most scattering experiments. Once you've got your approximately monochromatic incident wave, it will undergo interference when the wave hits the sample, and any subsequent measurement will not destroy the interference that's already occurred - what happens to the particle after detection is not of interest.

 

[Ziggurat]

The physical properties of a photon include that its momentum is inversely proportional to its wavelength. So a measurement of a photon's wavelength is the same as the measurement of its momentum. If you measure that a photon has an exact wavelength (i.e. momentum) then you lose knowledge of its position as the Uncertainty principle says.

There is an exception (not to the uncertainty principle, but to not knowing the wavelength): standing waves. Because you can have the same wavelength but different momenta (opposite directions) for a standing wave, you can get nonzero momentum uncertainty with exact wavelength in the special case of a standing wave. But that's clearly not applicable to the double slit experiment.