The title, the article, everything just screams scam. They never explain what they mean by the fourth dimension.
I am sure you are visualizing something sensible but reading that, to me, felt as ambiguous as the article.
Can you use a specific example with an actual physical 3D + extra dimension situation?
For instance, an actual example of a 4D-to-3D situation is the mapping of 3D space + 1D time to a 3D RGB color space, when representing the visual experience of a flying formation of LED drones.
Something that concrete?
you could come up with some material that naturaly has those kinds of properties without being wavy. but mathematically its the same thing.
> The phases of the space modulations can be used as adiabatic parameters that augment the physical space. It is intriguing to see these phases as additional global degrees of freedom, usually called phasons, living on a torus.
I still don't understand all the details of that sentence, but it looks like 4D is a correct technical term. [1]
The problem is using 4D in the press release, because it's misleading and clickbaty for a non technical audience. It's a weird 3D wave, that is easier to analyze if you map it to a fake 4D wave before doing the calculations.
[1] It looks like the kind of thing I would believe instantly if I heard it in a serious technical conference of physics. It makes sense and I heard similar weird stuff before. I need like 1 hour to read it carefully and perhaps take a look at other sources to be completely sure, but it's published in a serious journal, so my guess is that it's correct.
more supporting material. https://en.wikipedia.org/wiki/Phason
I don't understand anything about this field but I did used to know what "adiabatic" meant so forgive my lay interpretation... it seems the effects of a synthetic 4D are achieved, by varying these slices of the "periodic crystal of higher dimensions (up to 6)"... whatever that is... which is done changing the phase of "space modulation" in the material.
I think it's like: if you witness a 3D wave and you live in 2D flatland, you can still characterize the wave in 3D. And maybe you can even frob some knobs in flatland which change how that 3D wave behaves, e.g. by shifting its phase; changes in behavior in 3D which are observable in flatland's 2D "slices" also.
Phasons being on Wikipedia with no sniff of scam warnings there or in related articles, I'm inclined to believe the paper isn't a scam, whatever it's saying.
And a situation where the temporal behavior of waves are controlled across a 3D object would seem to be a sensible place to do it.
But the article doesn’t seem to be equating the “4th D” with time
It is just very unclear writing, or perhaps thinking.
Granted there's some clear ties and relationships between time and space, the classic x,y,z - well I would argue that the dimensionality of space probably amounts to more like approximately 3 integers-worth of connectivity-along-separable-axes in general (on average) but probably can and does fluctuate down nearer to 2 and beyond 3 in places!? Woo maybe slightly fringe way of thinking about space? But in my opinion time fundamentally doesn't (and probably cannot) work like that at all: Space is mostly symmetrical (in that +x is the same as -x, ignoring gravity for a sec) and can be moved-through by objects, especially those that control their own velocity. Time is not symmetrical (it seems, at all?!) and there is no control over the 'motion' of anything in time - causality is the engine making it 'tick' or 'go forward' (personal opinion of course).
I am not qualified to understand the paper but it does seem to me that given one could connect bits of string or wires (in our mostly-3d universe) into topologically-4d-networks.. maybe that is what this is more about? In this case the claim is that the material can do 4d wave-transmission IIUC which is a fair-bit more complicated than bits of string/wire. I don't think it's unclear thinking though, just a very complex topic!
>Common to all these is the existence of an intrinsic degree of freedom, the phason, which in many instances is experimentally accessible and fully controllable. The phason space augments the physical space and supplies additional virtual dimensions, hence enabling physical phenomena beyond what can be ordinarily observed in our physical space. In particular, the phason can be used as an adiabatic knob to engineer topological pumping, which is one of the main applications of the formalism, as evidence by the literature cited above.
https://www.nature.com/articles/s42005-021-00630-3
>Here, we formulate the theoretical principles and manufacture acoustic crystals composed of arrays of acoustic cavities strongly coupled through modulated channels to evidence one-dimensional (1D) and two-dimensional (2D) dynamic topological pumpings. In particular, the higher-order topological edge-bulk-edge and corner-bulk-corner transport are physically illustrated in finite-sized acoustic structures. We delineate the generated 2D and four-dimensional (4D) quantum Hall effects
https://www.nature.com/articles/s41467-021-25305-z
The other notion I see is to view quasicrystalline structures as lower dimension slices of higher dimension periodic arrangements:
>The structure of quasicrystals is best described in the framework of the superspace formalism, where the quasicrystal is embedded in a higher dimension (see Janot, 1992 ▸; Janssen et al., 2007 ▸, for an introduction). In the case of icosahedral (i) QCs, the superspace periodic lattice is defined in six-dimensions (six-dimensional) and it is decomposed into two three-dimensional subspaces: the parallel (or physical or external) space, An external file that holds a picture, illustration, etc. Object name is m-03-00247-efi1.jpg, and the perpendicular (or complementary or internal) space, An external file that holds a picture, illustration, etc. Object name is m-03-00247-efi2.jpg. The quasiperiodic atomic arrangement in An external file that holds a picture, illustration, etc. Object name is m-03-00247-efi1.jpg is obtained by an irrational cut through the six-dimensional periodic lattice decorated with three-dimensional objects, lying in An external file that holds a picture, illustration, etc. Object name is m-03-00247-efi2.jpg, called occupation domains (ODs) or atomic surfaces.