How serious should anyone take what is to follow? That is up to the reader. I am going to play around with concepts I find intriguing. But my interest is that of a layman who is likely to be trapped in the world of science fiction with no hope of making any contribution to real science. My maths suck. I have forgotten most of the classical physics I learnt at school, and my lack of aptitude for maths meant I never grasped even classical physics all that well. Quantum mechanics was always beyond me. Having said that, in recent years I have wanted to understand it. Maybe one day I will, at least to some extent, although that is going to depend on how diligently I finally get to grips with basic mathematical concepts, actually understanding them by working to understand most of the mathematical proofs at every stage. Not an easy task. I’m ashamed that it is only within the last few weeks that I finally understood a proof of Pythagoras.
I seem to have picked up bits and pieces from all over the place. Those ideas that I will deploy in this blog post that are not completely off the wall (and I’ve no doubt that many of them are) are almost certainly a regurgitation of what I have learnt subliminally. I doubt there much, if any, original content here: I have merely woken up to ideas that had been silently gestating in my brain, before they finally clicked. But in such circumstances I have forgotten when and where I read it. Who exactly deserves credit for proposing some of these ideas that may remain controversial and far from becoming common property of the physics community? I am not sure. I don’t want to put words in the mouths of serious scientists who would not wish to be associated with my half-digested idea, but I remember that David Deutsch and John Gribbin started me on the road to taking Hugh Everett III’s ideas seriously, as something more than fruitful science fiction. Nevertheless, despite my mega-amateur status, I want to explore a few ideas that do interest me greatly. If they do in fact turn out to be ideas my subconscious has unconsciously plagiarized from others, I apologize to those others. But, as I say, I make no claims to originality here, other than in pulling together other people’s ideas in a way that strikes me as a potential clue to what is going on with the double slit experiment, wave-particle duality and related matters of quantum mechanics. While there may be something here that is original, I would be as surprised as anyone else if that turned out to be the case. I will leave that to others whose grasp of this material is better than my own. Let them decide if this is not a matter of plagiarism (unconscious I assure you) of undigested ideas, mixed up with science fiction stream of consciousness diarrhea.
Wave-particle duality has to be related in some sense, surely, to extra-dimensions, dimensions to which we have no direct access. I have certainly come across illustrations that lead me to the idea that wave-particle duality is related to a helix moving throw a two dimensional plane. While I realize not every scientist accepts the existence of extra spatial dimensions, the idea of compactifiction (a la Kaluza-Klein, subsequently incorporated into the 10 and 11 dimensional string/M-theory framework) seems more than plausible, at least to me. How exactly a helix moving throw a compactified dimension would work is not something I can explain. My maths doesn’t come close to addressing such questions, and I know that those with theoretical rigour have identified major problems with Kaluza-Klein’s proposals. But let’s consider this from the perspective of an observer from four dimensional space-time looking at a helix cutting through Flatland.
If a scientist in Flatland had a piece of equipment that produced a helix, it would generate dots that can be shown to exist as discrete units. But at a different frequency, it would build up a wave-like pattern. Only from our point of view as an observer in four dimensional space time could this paradox be solved, since the very idea of a helix makes no sense to those whose experience of the world is limited to two dimensions.
But how does this relate to, say, the double slit experiment? Parts of this paradox are beyond me. However, if we see how we can explain mysteries that seem as weird as quantum mechanics do to us, then maybe this can provide us with a clue or two. Isn’t this worth at least exploring?
Suppose the helix generated by the Flatlander’s generator whose wave-particle duality we can fully grasp also still has a property or two that even we cannot explain fully, since we too are examining this problem from a perspective with one dimension too few. Suppose one problem was an apparent indeterminate direction of these initial helices. Suppose decisions have to be made to set up the equipment that will determine the direction of a helix, at least approximately, and that making such a decision makes it impossible for a Flatland scientist to simultaneously set up his experiment to test other aspects of this helix? I have a gut feeling that this might explain part of our double slit experiment. Not all of it, but a part.
The Flatlander would need to simultaneously explore different orientations to test these other aspects of the helix. But that is ruled out in principle due to his/her being unable to access this higher spatial dimension. Only higher dimensional observers, such as ourselves who can see what is going on, would be able to see that his equipment is generating phenomena that impact beyond his two dimensional frame of reference.
There are other aspects of the double-slit experiment that seem to suggest that much weirder things are going on. It does indeed looks like the electrons or photons are actually spying on the scientists, playing hide and seek with us. How can we explain this aspect of this experiment?
I cannot directly explain what is going on here. However, if our wave-particle duality is to be explained – in our four dimensional space-time universe – not by a three dimensional helix moving through a compactified fourth spatial dimension, but by a four dimensional helix… What would that mean in precise terms?
Is it possible that what looks to us like three dimensional waves are actually mere shadows of something much more fundamental, something beyond our experience? Can brains evolved to deal with the impressions offered by our senses make sense of such concepts? Are our brains deaf and blind to phenomena totally irrelevant to the needs of our species during its formative years when it liberated itself from our ape-like ancestors? Might our brain not have evolved to fill in the gaps our senses leave behind? While good for most purposes, might our brains have no option but to provide us with the conceptual equivalent of an optical illusion? Might wave-particle duality not have something to do with that?
Maybe reflection, refraction and diffraction are limited glimpses of something else: the interactions of very many four dimensional helices? What might such interference look like? I don’t know. No one whose senses and brain evolved to deal with a world of three spatial dimensions can know what this would look like. Nevertheless, many computer simulations could produce answers, possibly. Computers help us understand four dimensional cubes, hypercubes, tesseracts. Maybe we could even produce virtual reality 3D goggles that allow us to experience how a 3D human might move within a 4D terrain with single photons/electrons appearing as a helix slicing through a plane. Maybe computer simulations could make best-guesses as to how 4D helices could interfere with each other, and how there could be laws of how this could produce the shadows in our 3D universe that appear to us as reflection, refraction and diffraction. If we could do such a thing, additional phenomena which we did not anticipate might suggest other shadows that would appear as a consequence in our 3D universe. And maybe we could infer from this potential answers to how our photons and electrons appear to be spying on us when we conduct our double slit experiment. The best idea I can come up with is that some magnetic field is produced in the detector that affects the original experiment, but I can only assume scientists have eliminated that as a possibility.
All this would produce are explanations that would would not – yet – be amenable to testing directly. To get direct evidence, we would need to set up instruments that could test theories based on observation of interference of four dimensional helices. But we don’t know how to build such devices, nor see the results. And that would be a function of our inability to directly access these compactified extra-spatial dimensions, the ones that photons and electron appear to be capable of moving through.
Possibly an intelligent observer who had freedom to move within the fourth spatial dimension could watch individual helices and the simultaneous production of several such helices interfering with each other – producing equivalents of reflection, refraction and diffraction, and possibly other phenomena with no three dimensional equivalent. That may hold the key to what happens when we watch individual photons in the double slit experiment. Is this such a bizarre idea? If it is, then my understanding of the problem is clearly a lot worse than I had hoped.
But how could a helix produced one at a time interfere with one produced at a subsequent time? An understanding of that would be required to produce any kind of interference pattern, right? How do we know that our equipment is producing only one photon at a time? Maybe the Flatland scientist is producing several helices at a time. However, his/her limited point of view makes it impossible for him/her (but not us) to access more than one aspect of this problem at a time.
If more than one helix was being generated simultaneously, presumably they would be heading in different directions, away from each other. However, is it not possible that there could more than a single Flatland, each with an inability to perceive their parallel universes? Is it not possible that a helix generated in one Flatland is interfering with a helix produced in a neighboring Flatland parallel to it?
Maybe Hugh Everett III’s ‘Many Worlds’ interpretation of quantum mechanics explains why two scientists are aligned simultaneously engaged in very nearly identical double slit experiments, with each of them generating helices, each creating an interference pattern thanks to the behavior of his/her closet neighbou . Possibly he/she is doing this with neighbourhood Flatland scientists on either side of the ‘hypothetical’ z-axis of a hyperspace of three spatial dimensions.
And possibly the helices that are generated are not just interfering with those produced by scientists in the closest parallel universe. Maybe each Flatland scientist is producing four dimensional helices that interfere with an endless stream of four dimensional helices produced by dozens, scores, millions of almost identical copies of this Flatland scientist. Is that so far fetched? Maybe the idea of compactification seems impossible to explain such phenomena because all this does is explain the gateway through which photons and electrons etc can influence parallel universe, but that the scientists in each parallel universe have access to much more three dimensional space than we can directly access. Look at this problem from the perspective of ourselves looking on at the limitations of the Flatland scientists and the problem could be understood. Right?
One last point…
Do we even have to refer to interference of four dimensional helices to explain part of the double slit experiment? A single helix cutting progressively through a plane yields both particle-like and wave behavior that is only understood by those of us who experience a third spatial dimension. Could a single four dimensional helix not generate a pattern as it slices through our narrow three dimensional universe that builds up into a wave-like interference pattern, despite its actually being a great deal more than either a point particle or a wave, but something richer and much more fundamental: a four dimensional helix slicing through our three dimensional space? And what if the maths ‘proves’ that four dimensional helices are incapable of interfering with each other the way three dimensional waves can? Maybe the answer is that we are in fact dealing not with four dimensional helices in four dimensions of space, but something involving even more than four spatial dimensions. Maybe computer simulations could unpack when this might work, or maybe our four dimensional space-time computers won’t be able to create simulations at all as at these higher dimensions the laws of physics create new physical phenomena that defy logic produced by senses and brains developed to grapple with the problems of three spatial dimensions.