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This question will be in some way complicated for different reasons - I am no physicist, I know about things like wave-particle duality, that the tranversal wave motion comes from change in electric field strength and magnetic flux density but I have no good imagination about all of it. So I will try to add further question that I probably will need answers to to get a sufficient answer to the title question.

What means observing in sense of wave-particle duality. When does a quant feel observed.

Why does a quant want to do a transversal motion by still maintaining the actual motion direction (ignoring gravitation which should effect the photon/quant because of its kinetic energy) - and how do they do it without loosing kinetic energy.

The answer at some point will probably be you consider particle properties at one point and wave properties at another point. Or you think about a model created to represent a certain property and draw conclusions from this model exceeding the actual limitations such a model has.

So I would like to understand when is light a wave and when it is a particle and if it is always both then when does it have certain properties, when does it loose them and when does it gain different ones instead. (Could it loose wave and particle properties - and what would be left of it in that case?)

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I start with a word that I see in the title: "transversal". I guess that it refers to the "transversal" polarization of the electromagnetic wave. It does not mean that there is a "transversal movement": it refers to the fact that the polarization is perpendicular to the direction of propagation. Practically, on macroscopic scales and in usual situations, light can be often considered as formed by rays (geometrical optics) which propagate linearly, without any "transversal motion". So, what is "transversal"? The electric and magnetic fields. If you observe a point hit by the ray, you observe an oscillating electric field, perpendicular to the propagation. For example, if you put an electron along the ray, it will be accelerated perpendicularly to the propagation.

There is no difficulty in imagining a very thin ray. It would not have to do with quantum mechanics. But it is also easy to imagine a photon as a very small object, characterized by an electric and a magnetic field as a ray of light.

About gravity. Electromagnetic waves (quantized or not) are deflected by gravity. However, this is not because they have a mass (that they do not have), nor because they have a kinetic energy.

Finally, when an object is a wave and when it is an object. This is a too big topic, better to read a book on quantum mechanics. But to make it simple, you can imagine light as a flow of sand. As you see it in large amounts, it looks like something continuous, but if you look carefully, you see the single grains. Analogously, light appears usually as a wave, except when you have a very small intensity and very sensitive instruments: then, your instruments will start to detect single flashes rather than a continuous flow of light. Of course, very roughly.

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