In my view, the reason we can't transmit smell is that we don't understand it. That is, we don't have a solid understanding of how odor information is coded, so it is hard to imagine how to build a system that could reproduce that information.
This is sometimes discussed in terms of a multi-dimensional "odor space," where each odor could be described by its location along each dimension. The problem is that we don't really know what any of the dimensions are. By contrast, we know that visual space can be described by the intensity of a set of colors in a two-dimensional plane; auditory space is described by frequency and amplitude. It is clear that odors are comprised of chemicals, but we don't yet know where those chemicals fit in odor space. Understanding the odor space is a prerequisite to building a system that could transmit messages from it.
Also, to a great extent, how to engineer a smell transmission system is only partly a biological question. For instance, a CMYK printing system does a fine job at generating images that our RGB photoreceptors understand just fine. A telephone wire can transmit sound without a care about how the cochlea actually works. Transmitted pictures and transmitted sounds work because they activate our photoreceptors and auditory hair cells in the same pattern that the original images and sounds would. We can build systems to do this because we understand the nature of the information sensory systems decode, and we don't need a really deep understanding of the physiology to do that. (Of course, I think figuring out that physiology is great fun, but that's another point.) That is, to build a smell system, it's probably not really necessary to know what every one of the many olfactory receptors does. That's a detail of the way the mammalian olfactory system evolved. The important thing is to understand the nature of odor information. Then it really may be theoretically feasible to create a system to transmit odors.
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