In standard QM, photons are waves, but in Bohmian mechanics, photons are particles being guided by waves. So, if you split the wave, do you also split the particle? How would that work?
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Contrary to popular belief, we cannot split a photon. Photons do not decay, and cannot be split like you split a nucleus for example.
There is no natural decay of the photon due to conservation of momentum and energy. If it split into two photons their added four vectors would have an invariant mass.
Though, what you might be referring to, is called Spontaneous Parametric Down Conversion, and is used quite frequently to produce entangled pairs of photons.
Spontaneous parametric down-conversion (also known as SPDC, parametric fluorescence or parametric scattering) is a nonlinear instant optical process that converts one photon of higher energy (namely, a pump photon), into a pair of photons (namely, a signal photon, and an idler photon) of lower energy, in accordance with the law of conservation of energy and law of conservation of momentum.
https://en.wikipedia.org/wiki/Spontaneous_parametric_down-conversion
Now you are asking about Bohmian mechanics and how it would explain the splitting of the wavepacket. There is a interpretation that tries to do exactly that, and in this case, the explanation is that the wave packet (having only a single photon) enters a beam splitter, and splits into two smaller wavepackets. In this interpretation, one of the wavepackets has the particle inside it, and the other wavepacket is empty.
Árpád Szendrei
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Let's take a look from the other direction. The wavelength and the photons energy are connected. To preserve energy when splitting a photon, two photons of half the energy have to emerge. In wave representation that would come out as doubling of the wavelength, so you would not split the wave, you'd rather change its form.
Splitting of the wave, however you want to achieve this, will result in a change of the trajectory of the photon.
