Why do we say photons travel ?

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It never exhibits its wave and particle natures simultaneously.

Good point. I had never fully considered that. I guess it depends in part on what is meant by "exhibits."

Can one realize a photon's pure wave nature from its nonsimultaneous and pure particle nature?

Is a wave packet a single photon imaginary in part, or perhaps always a multiplicity of photons?

Might wave packets interact with other wave packets?
 
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... if you try to observe the wave nature of a photon and then try to observe its particle nature... how do you know you are still looking at the same photon? don't they all look pretty similar...

I would say science is about measurement, all we can know is what we measured in a particular interaction and we can only try to guess (educated) what happens between measured interactions...
 
Loren Booda asks,
Is a wave packet a single photon imaginary in part, or perhaps always a multiplicity of photons?
I'm not sure what you mean by 'imaginary in part'.

It might seem intuitive that you can produce a photon by chopping a light beam into a very short pulse of light. The result will have a spread of frequencies ( Fourier modes ) and looks mathematically like a wave-packet, a wave packet being a superposition of many close frequencies. It is also localizable like a particle. But it is controversial to refer to that as a photon.

Single photon sources are notoriously difficult to make, and I haven't seen completely convincing experimental results, but I may not be up-to-date with the technology.

axawire, I agree with your view that we can only guess what goes on between obervations.
 
Is a wave packet a single photon imaginary in part...
In other words, can't the photon before measurement be represented as a vector oscillating in complex space? A Fourier transform, such as accompanies a measurement, might convert a wave packet into a photon, or a wave into a wave packet.

Single photon scintillations have been observed for decades.
 
Branching this question

lightarrow said:
Can a photon exist in absence of interaction? Perhaps we should start a new thread about it. (My answer is no, but I'm open to every possibility).

I think it might be beneficial to mkbh_10's question if there is agreement on terminology. I've posted this question as "When is a photon a photon"