This is not a foolish inquiry, and I agree with @Michael_Callen that @structureoftruth did not imply that you are a fool for asking this.
Here are my comments on your inquiry:
Pocket dimensions are exactly the way that modern physicists understand all forces in nature with the exception of gravity. This is a somewhat new technology (~50 years old) and I am delighted+surprised that a layperson would know of it. Note that these pocket dimensions are related but distinct from the extra dimensions of String Theory (which are hitherto unobservable). On the other hand, these pocket dimensions lay at the basis of the Standard Model of particle physics, a theory which has been experimentally tested to unprecedented accuracy (our own @dga471 works on these experiments).
However, in mainstream physics, these pocket dimensions are not something that veiled light particles in a picture where the light particles are somehow embedded in a wave. Rather, the electromagnetic field (which constitutes light), is the consequence of the existence of these pocket dimensions.
@PdotdQ, are you referring the the internal degrees of freedom for the quantum fields, on which the gauge symmetries (U(1), SU(2), SU(3)) act? I have never heard them called pocket dimensions before, and it seems to me a bit odd to conceptualize them as being like extra spatial dimensions. (They are more like quantifiable charges or properties that the field can have, or components of the field value, are they not?)
@gbrooks9 It occurred to me that something much more accurately described by “particle embedded in a wave” would be a theory where there is a field (in physical 3-space) which contains mobile singularities acting like particles; I’ve read that de Broglie (who originally came up with pilot-wave theory) hoped he would eventually find such a model, and considered pilot-wave theory a stepping stone towards it.
As far as anyone knows right now, though, such a model would have no way of producing the non-local correlations that we see between entangled particles. That is why the “wave” in pilot-wave theory is the wavefunction, existing in configuration space rather than physical space.
Yes. Particle physicists typically don’t call them pocket dimensions, but that’s exactly what they are. For example, adding an extra spatial dimension combines general relativity and electromagnetism. If you compactify this extra dimension, this extra dimension becomes ~U(1), which gives you the usual picture of U(1) being the gauge symmetry of E&M (if you are familiar with the language, this turns spacetime into a principal-U(1)-bundle). From here, it is a short jump to generalize from U(1) to any other gauge symmetry that you want. Note that the actual technical challenges to do this is not a short jump.
Most people do not learn this very geometrical language. Most people learn the gauge symmetries as connected to the internal degrees of freedom of quantum fields, like you mentioned. As long as some conditions are satisfied, these two pictures are identical. One is more geometry-heavy, while the other is more representation theory-heavy. You can guess from that which one is favored by relativists and which one by particle physicists.
Modern physics actually suggests the other way around: your extra dimensions (which may or may not be spatial, i.e. can carry a different “length” unit than cm, m, etc) are folded up within the 3 spatial dimensions + 1 time dimension that consists of everyday reality (what physicists call spacetime). By this I mean that every point in spacetime contains these extra dimensions attached to it.
I am trying to understand what you exactly mean by this; perhaps a picture is required. If I understand you correctly, you were saying that it might be possible that wormholes are objects that connect two points in spacetime that do not have a “length”, i.e. it is a point of contact between the “two-folds of spacetime”. Is this what you have in mind?
Great! These types of wormholes are not prohibited by general relativity, though not because of the reason you state:
Further, while general relativity itself does not have any prohibition against wormholes (of any types), inputs from other parts of physics (and sometimes philosophy) argue against both the “tunnel” and “contact” wormholes.
Note however, that the “tunnel” type wormholes are way more feasible than the “contact” type wormholes that you favor. This is because the nonexistence of these tunnel wormholes rely on the validity of some physical properties that might not hold in the quantum realm. On the other hand, the “contact” wormholes require in addition that the Universe possesses a condition that imposes a nontrivial shape in an ad-hoc manner.
To me an entangled pair of particles is a single particle that appears one way in one fold of space with an opposite reflection appearing in another fold of space.
The whole point to multi-dimensional manipulations is that a tunnel is not actually necessary.
When people use the famous example of folding a sheet of paper to show how fast travel can be if you fold space… i dont recall anyone mentioning a tunnel as an entailed necessity.
A “tunnel” is an example of these “multi-dimensional” manipulations.
As I mentioned, that possibility is allowed by general relativity, but it does require some ad-hoc conditions to be imposed on the manifold. However, your previous comment refers to particle entanglement. This situation is much more complex then the simple “folding a sheet of paper” example.
From your previous comment:
Entanglement clearly cannot be explained just by one particle being seen in the forward facing and backward facing holes of a wormhole. If so, how would you explain entanglement of non-identical particles?
In addition, note that the “paper folding in space” is just an oversimplified analogy to explain wormholes to the lay audience. As with any oversimplified analogies, one cannot push it too far.
Yes… i suppose that is quite true. But if there is ever to be true that a particle or event occupies or traverses more than 3 spatial dimensions at once… my view is that such a “thing” would not need a tunnel at all.
Ironically… “sustained travelling” (like a star ship Enterprise) not only seems less likely… but would seem to be more in need of a “tunnel” than entanglement.
This sentence is confusing. Of course if a particle or event occupies more than 3 spatial dimensions there is no need for a “tunnel”. The “tunnel” only refers to when a wormhole appears. Note that I am using the word “tunnel” because you used it in your original post. No physicists call the tunnel a “tunnel”, rather we call them the “throat”.
Are you talking about warp drives now? That’s a different thing entirely. It’s unclear what a “tunnel” even is in this case.
A lot of these things are not intuitive, that’s why we use formal mathematics in this field so that our intuition does not lead us astray.
This is not what physicists mean by entanglement. Quantum entanglement is the situation when the quantum state of a group of particles are correlated, i.e. the quantum state cannot be broken up into its constituents.
I believe this approach will eventually be replaced with the idea that a single particle (with unbroken constituents) can be better interpreted as existing in two places simultaneously in our first 4 dimensions because they have been given unifying coirdinates in a higher spatial realm as a SINGLE enyity.