Regarding Photon and Matter Wave relationships this may be informative....
So matter charge and mass can convincingly be produced from only light which has no "native" mass... Matter from energy alone. So where did that mass come from? It has come from a symmetry operation. This is the CPT-Lorentz Symmetry where the charge, parity and time "cooperate" to form spin orthogonal particle couples that have sources of charge and all sources of charge seem to have mass even though in some cases it is an exceedingly small mass. A reasonable person may conclude that light creates mass and charge from its own "primary electromagnetic substance". So why does mass attract other mass? Answer: For the same reason that light is attracted to mass... and it is if it is allowed to "fall freely" near a massive body and was one of the first tests of Einstein Special and General Relativity. The experiment which has been done many times indicate that the attraction between matter and light exists "already"... even without any mass in the universe. what does this really mean? If photons attract mass with purely electromagnetic influences then why not photon on photon... Well this does happen too. All photons of the same wavelength on the same wavefront that are coherent (co-moving) attract each other with an "infinite influence" (in the transverse direction) and so all co-moving coherent photons all exist in the one inverse square law expanding boson state. Any such "attractive" influence acting on a "massless particle" will cause an infinite acceleration and very quickly any two separate photons will be one state and cohabiting the same space. Experiment support this fact and light obeys Bose-Einstein Statistics.
While matter particles
attract each other they are limited in their attraction by their inertia (mass... which is their reluctance to move or to resist acceleration at an infinite rate). However why doesn't a photon accelerate toward another "particle with mass" with an infinite acceleration too? (it turns out it is the same acceleration that all "light particles" (photons) are attracted to a massive object). In a vacuum a rock a feather and a photon of light have the same acceleration toward a massive object, it is just their initial velocities that cause their obvious difference in properties.
Of course two massive objects have "mutual" influence on each other as well so this experiment can't be extended to all planets and stars because each particle of mass has mutual gravitational influences between their component resources. This influence between "mutual" masses is directly related to their individual curvature of spacetime that each one produces. Each mass source contributes to the overall mass of a "massive collection of particles" cumulatively. In the final analysis the mass is the measure of potential energy of a system. Two particles in a system can lower the overall potential energy by coalescing. This can only occur if the kinetic energy of the two systems remains zero. Usually this process will dissipate some kinetic energy.
Considering the internal and external relationship of a surface to it's space the external spacetime of any mass particle must be "positively curved" while the "internal spacetime" of the same particle could be considered as the internal surface which would be relatively negatively curved. If some relationship between these two surfaces exists as suggested above then Electromagnetism is a denizen of the two dimensional inner surface
and Gravity is a denizen of the outer three dimensional space surface
(ignoring time). It is clear that the two dimensional inner surface space of a "bubble" as a surface will not allow for the packing of three dimensional objects into it as does the external space of particles... or does it? The "conjecture is that the "apparent" two dimensional surface "appears" three dimensional to inhabitants of the surface, a kind of "flatland" as described by Abbott. The laws of packing in that surface are the laws of electromagnetism which relate to Bosons (Bose-Einstein Statistics) while the external spaces which are three dimensional relate to the laws of Fermions which obey a different packing relationship of Fermi-Dirac Statistics... The way billiard balls stack. This is the way we think our world "appears" to us... Three Dimensional with Time.
Now lets think of the Story ... Alice Through the Looking Glass by Lewis Carroll.The Looking Glass House
It is possible to conceive that as Alice is in her world the looking glass is to another world that is related to our world but very "flat"... To Alice the looking Glass House would appear Flat but it obeys all the rules of our world (Universe) with one exception... it is all reversed... It is an Anti-World. The next point of difference is light does not obey the laws of physics that matter obeys... What if the anti-world in the mirror was not a world of light "waves" but a world of matter "waves"... de Broglie Matter Waves. That "image in the mirror" would then be the result of material matter and not simply visible light. If it were so then these would behave like "Condo Phantoms" of our world and could in principle partake in the same physics that matter in our world can. It has been noted that such phantoms can exist and partake in chemical reactions with matter from our Universe. This experiment can only be partially performed with Quantum Corrals... the mirror is a not an optical mirror but a ring of encircling atoms and an atom is placed at one focus of an ellipse ad the phantom "appears" at the other foci. Because the "corral" is not perfect... it is more like a fence around a a flat paddock... rather than an all encompassing ellipsoid of revolution the "image" is actually at a lowered "amplitude" to the source amplitude... however for all intents and purposes the particle's image has all the attributes of the original particle which could be an atom. This phantom atom has been subjected to chemical reactions and will enter into molecules that are half phantom and half real. These are matter wave replicas of the original.
Getting back to Alice and her Looking Glass House... A "perfect" matter wave mirror may be capable of not only recreating the entire external universe "up to a point" the image would be capable of independent physics because it is not just an optical image but a matter wave image. If Alice "could" squeeze into that world she may be able to exist in that two dimensional surface as if it was a world of higher dimensions as if it was a matter wave world rather than a bosonic world. The physics of "our" normal three dimensions would become the physics of the apparent two dimensions through projection or a rotation into/onto the surface (hypersurface). Movement in the additional dimensions would be possible with a change of scale "in" the surface. Alice may find another Alice in there and also find some differences in the Physics if the Looking Glass House was a matter wave reproduction of her former Universe (world) instead of an optical "copy"... Just like Condo Phantoms in Quantum Corrals.
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Extending this conjecture further... the Looking Glass World to us appears as a simple optical surface if it were curved it would cause a deformation like in a lens... the suggestion is what is the geometry of of a Christmas Ball world...
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This is Dali's reflection in a crystal ball.... Actually it is a reflection in a silvered surface ball like a Christmas ball. Now modify this "ball" to image matter waves as a reciprocal space in the same way that de Broglie waves are the reciprocal of normal waves. This would mean that large objects would be small and small objects would be large and the entire Universe (world) would "fit" into this mapping... I would like to take this one step further it should conform with a Fourier mapping of the external space into that internal space. This maps distances in our world into reciprocal distances and time into frequencies. This is what happens with an optical fourier processor such as this one...
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This is a simple optical device that processes transparent two dimensional images into the transform plane where it can be "filtered" to remove an artifact using a spatial filter (a mask placed in the transform plane). The image is recovered filtered and all at the image plane.
So we have two different views of the same world. One world is the familiar one in which everything is three dimensional and matter seems to be very real. The other world is one where from our frame of reference "can't be real" since it exists in a surface and yet apparently obeys all the laws that our three dimensional world exhibits in a flatspace. From the perspective of "something" in that flatspace it would "see" everything as if it were three dimensional. The conjecture is our Universe is this kind of flatspace with Universes "above" and "below" in which physics is progressing as entangled phenomena relative to events executing in parallel worlds at all scales. Everything is then "matter wave optics".
From our "external" perspective the "reflections" in Looking Glass Ball Worlds are embedded in a flatspace and exhibit some kind of "surface phenomena" physics.. a physics of scalar inner product ... a projection of the physics and "optics" of our world... while in our world these "similar" phenomena exhibit mass and gravity. There is also the enigmatic (bosonic) electromagnetic phenomena that are also responding to cavity resonant states in the same space as the mass and gravity we are seeing around us. The conjecture is this electromagnetism is propagation on the inside of a dimensionally closed cavity... very similar to the externally seen "flatspace" of a Christmas bauble. In the very same space we also see "external" Gravity and Mass states which result in some apparent forces of gravitational attraction.
So what we have is a flatspace for "bosonic" electromagnetism that we see as standing waves filling a space inside a cavity Universe that appears as actually a flatspace to observers that are external to our universe. At the same time we are external observers of the gravity and mass of external spacetime curvature in our three dimensional fermionic universe around us. At a higher perspective these mass and gravity fields are seen as flatspace events not of gravity and mass but of bosonic phenomena.
A symmetry which has a bosonic shadow of a fermionic universe followed by a fermionic shadow of a bosonic universe in successive layers of a matter wave "bubble". The inside of a bubble is bosonic and allows the propagation of electromagnetism and the outside of the bubble ... all the way to "infinity" we have the rest of our three dimensional Universe sharing 4 dimensions with these "shells". At the same time out mostly empty universe not only has matter in it it also has light indicating the internal surface (...or a matching flatspace of something).
We interpret this as light spreading through the inner cavity of a huge "flatspace" as far as we are concerned (electromagnetic propagation). That EM propagation is simply a global "exchange force"
in this bubble universe. Around us (including us) there are matter particles sparsely occupying the "bosonic" space (planets and galaxies) which are the outside connection between these matter particles. The force in this Universe is Gravity and this arises through "mass". There really is no direct connection between the Gravity and the electromagnetic forces since one has no property of mass and propagates on the inner surface of "sub atomic particles" and the other is a property of de Broglie waves on the "opposite surface" of the Universe. The two surfaces are connected "reciprocally" through a transform... the two realms are particle and wave and have different descriptions depending on which side of the manifold is being described. The transition from one domain to another results in a change in geometry from standard geometry of ordinary space to reciprocal space and reciprocal time (frequency).
For each and every boson here is a fermion and for each and every fermion there is a matching boson. The fermions are sub-atomic particles (with mass) and their matching mirror world bosons (without the mass) hybridize in place as space filling waves and this influence fills space with unseen standing boson waves At the same time the nucleus also form hybridized matter waves in space. Boson hybridization are the shells of atoms and house electrons and clumping of sub-atomic fermion particles are all the nuclei of the atoms.
So the original question above is the massless boson photons do transfer mass since the mass is a property "seen" on the opposite side (surface) of the spatial curvature of the sub-atomic particles "bubble".
I know that is going to cause some ruckus by all those who are self appointed guardians of the morality of Physicists but I ask you all to think about the results of physics and see that this matches our current range of experiments without any direct contradictions. This interpretation will not change Quantum Electrodynamics since it is an optical theory and quantum gravity is no longer a problem since we will not be quantizing space anymore at small scale but will treat it as a continuum of reciprocal entities where what is big in our world is small in the "sub-atomic" world and visa versa. More energy simply "probes" the sub-atomic mirrors at smaller scale. This is what we actually see. Small physical size in sub-atomic systems
means higher energy and large size means low energy, The Universe when it is all considered is really composed of sub-atomic particles and that means that the behavior of the Universe is the behavior of these sub-atomic particles when they clump together. No Planck Limit.