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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2When the Bohmian wave splits, the particle will be in one part of it and will be guided by that part. The other part of the wave will be irrelevant to the particle's future unless the two parts recombine. – Mitchell Porter Jun 22 '20 at 10:49
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@Mitchell Porter But that would contradict Spontaneous Parametric Down Conversion, because two different particles are created in reality. – Jun 23 '20 at 02:26
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1What I said is valid for a process like the double slit experiment, where there is only one particle from beginning to end, but the wavefunction is divided. As Arpad said, SPDC is a more complicated process. Since it indeed results in more than one particle, it doesn't just consist of splitting a wave, bur rather in the creation of a two-particle wavefunction with twice the degrees of freedom of a one-particle wavefunction. You may wish to read about "Fock space". – Mitchell Porter Jun 23 '20 at 05:20
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A late extra comment: there is no standard Bohmian electrodynamics, but if there were, the classical part of the ontology would probably be a field, not a particle, i.e. QED would be explained as an ontologically classical electromagnetic field with a nonlocal component to its evolution, rather than in terms of photons. – Mitchell Porter Feb 26 '21 at 07:32
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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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But wouldn't it contradict observations, then?? Because in the SPDC, the photon is converted into other photons. Wouldn't that imply the other wavepacket should not be empty but instead contain another particle with half energy? How can it be empty if there are other photons? – Jun 23 '20 at 02:23
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2@Physics SPDC is a special crystal, that is different from a beam splitter. In the SPDC, the photon is absorbed, and it's energy is re-emitted in cascades, two photons. The beam splitter is different, as it mainly works by reflecting and refracting some of the photons in the beam. – Árpád Szendrei Jun 23 '20 at 04:35
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Ohh, I think I'm starting to understand. So, the photon is absorbed, and then two photons are re-emitted. Perhaps, when this happens, a new wave-function would guide the new photon! :) Thanks for your answer. It was really helpful! – Jun 23 '20 at 17:00
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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.
