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In scattering experiments, for example light scattering, the scattering strength from different sized particles is depicted as below.

Scattering examples

What I can't understand is: how does a particle know which direction the light is coming from and therefore which direction to bias the scattering (as in the case of large particles)? For instance, if we are just thinking about the electron oscillations, don't they just occur perpendicular to the light source?

So in my example below, I have a particle being illuminated from the left, and one from the right. If we were to look at JUST the electron oscillations inside particle, wouldn't they be doing the exact same thing? So how does the scattered wave seem to 'know' where 0 degrees is in relation to the incoming beam?

For clarification I am not talking about the angular dependent interference due to Rayleigh or Mie scattering. I hope this makes sense.

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Second Law of Thermodynamics ? –  Waqar Ahmad Jul 30 at 7:40

3 Answers 3

up vote 3 down vote accepted

It is momentum that defines the incoming direction and momentum transfer the outgoing one.

The photons, quantum mechanically carry momentum equal to p=h*nu/c . Momentum is a vector and defines directions.

An electromagnetic field is an emergent classical quantity built up by innumerable photons.

There exists also a momentum defined for the classical field where the Poynting vector defines the direction, if one ignores the quantum dimensions, but you are talking of electrons which are quantum mechanical elementary particles.

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Thanks, I have only ever studied the classical description of light scattering - via the solutions to Maxwells equations. From this view it never clicked how the oscillations know which direction the field is going, but I guess the Poynting vector is the answer for that. Out of interest is the a completely classical visualization technique? I can still only imagine a sustained dipole oscillation... –  Steve Hatcher Aug 3 at 15:54
    
The classical frame does not know about electrons and atoms and worry about dipoles or quadrupoles. It has indices of reflection and refraction , absorption, emission, all collective descriptions. –  anna v Aug 3 at 18:22

Let me offer you a slightly modified version of your question to illustrate a way of re-formulating it your thought process.

How does a pool ball know from which direction the cue ball hit it?

The answer is the same in the sense that "the particle" does not know all by itself, "the system"1 has certain invariant quantities (like momentum and energy) and some of those are vectors and have directions built in. Just like the cue ball, the incident light carries energy, momentum and angular momentum and those conserved quantities must be respected by final state of the system.

This approach is, perhaps, more natural if you use a quantized (i.e. photons) picture of light but it still applies with a classical view in which the energy and momentum input is continuous.


1 That is the "the particle" and the incident light or the combination of the two pool bals.

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OP does not want pool balls but some fundamental particles (inside) phenomena. –  Waqar Ahmad Jul 30 at 7:41
    
@WaqarAhmad The point is that it is not fundamentally any different. Both systems have to conserve momentum and that is what sets and communicates the axis of the interaction. –  dmckee Jul 30 at 21:31
    
This got me thinking for a bit, so thanks. I realize its the concept of electromagnetic wave momentum I really need to brush up on... –  Steve Hatcher Aug 3 at 15:54

This is just a complement to the previous answers which give the correct response. If you want to think about it in an intuitive way, imagine that the interaction between electrons and photons becomes weaker. In the limit when it becomes nearly zero, the light will be almost not scattered at all and will continue in a straight path.

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