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mpc755

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  1. Because understanding wave-particle duality is a moving particle and its associated wave is too complicated... "While the founding fathers agonized over the question 'particle' or 'wave', de Broglie in 1925 proposed the obvious answer 'particle' and 'wave'. Is it not clear from the smallness of the scintillation on the screen that we have to do with a particle? And is it not clear, from the diffraction and interference patterns, that the motion of the particle is directed by a wave? De Broglie showed in detail how the motion of a particle, passing through just one of two holes in screen, could be influenced by waves propagating through both holes. And so influenced that the particle does not go where the waves cancel out, but is attracted to where they cooperate. This idea seems to me so natural and simple, to resolve the wave-particle dilemma in such a clear and ordinary way, that it is a great mystery to me that it was so generally ignored." - John Bell
  2. I'm under the impression that I am talking to people who are capable of understanding "No Empty Space in the Universe" means no empty space in the Universe. 'No Empty Space in the Universe --Dark Matter Discovered to Fill Intergalactic Space' http://www.dailygalaxy.com/my_weblog...ic-space-.html "A long standing mystery on where the missing dark matter is has been solved by the research. There is no empty space in the universe. The intergalactic space is filled with dark matter."
  3. Exactly. That's what "No Empty Space in the Universe" means. 'No Empty Space in the Universe --Dark Matter Discovered to Fill Intergalactic Space' http://www.dailygalaxy.com/my_weblog...ic-space-.html "A long standing mystery on where the missing dark matter is has been solved by the research. There is no empty space in the universe. The intergalactic space is filled with dark matter." "No empty space in the Universe" means no empty space in the Universe. That's why I always place quotes around 'empty', to note that the space which does not consist of particles of matter has mass. - - - Updated - - - What is thought to be virtual particles is actually the chaotic nature of the dark mass. For example, the following hydrodynamical representation of the Casimir Effect is analogous to the chaotic nature of the dark mass. 'Water wave analogue of the Casimir effect' https://upload.wikimedia.org/wikipedia/commons/9/9d/Water_wave_analogue_of_Casimir_effect.ogv NON-LINEAR WAVE MECHANICS A CAUSAL INTERPRETATION by LOUIS DE BROGLIE “Since 1954, when this passage was written, I have come to support wholeheartedly an hypothesis proposed by Bohm and Vigier. According to this hypothesis, the random perturbations to which the particle would be constantly subjected, and which would have the probability of presence in terms of [the wave-function wave], arise from the interaction of the particle with a “subquantic medium†which escapes our observation and is entirely chaotic, and which is everywhere present in what we call “empty spaceâ€Â.†The “subquantic medium†is the dark mass. ‘Fluid mechanics suggests alternative to quantum orthodoxy’ http://newsoffice.mit.edu/2014/fluid-systems-quantum-mechanics-0912 “The fluidic pilot-wave system is also chaotic. It’s impossible to measure a bouncing droplet’s position accurately enough to predict its trajectory very far into the future. But in a recent series of papers, Bush, MIT professor of applied mathematics Ruben Rosales, and graduate students Anand Oza and Dan Harris applied their pilot-wave theory to show how chaotic pilot-wave dynamics leads to the quantumlike statistics observed in their experiments.†A “fluidic pilot-wave system†is the dark mass. ‘When Fluid Dynamics Mimic Quantum Mechanics’ http://www.sciencedaily.com/releases/2013/07/130729111934.htm “If you have a system that is deterministic and is what we call in the business ‘chaotic,’ or sensitive to initial conditions, sensitive to perturbations, then it can behave probabilistically,†Milewski continues. “Experiments like this weren’t available to the giants of quantum mechanics. They also didn’t know anything about chaos. Suppose these guys  who were puzzled by why the world behaves in this strange probabilistic way  actually had access to experiments like this and had the knowledge of chaos, would they have come up with an equivalent, deterministic theory of quantum mechanics, which is not the current one? That’s what I find exciting from the quantum perspective.†What waves in a double slit experiment is the dark mass.
  4. 'Dark matter' is now understood to fill what would otherwise be considered to be empty space. Meaning, 'empty' space has mass. 'Cosmologists at Penn Weigh Cosmic Filaments and Voids' http://www.upenn.edu/pennnews/news/cosmologists-penn-weigh-cosmic-filaments-and-voids "Dark matter ... permeate all the way to the center of the voids." 'No Empty Space in the Universe --Dark Matter Discovered to Fill Intergalactic Space' http://www.dailygalaxy.com/my_weblog/2012/02/no-empty-space-in-the-universe-dark-matter-discovered-to-fill-intergalactic-space-.html "A long standing mystery on where the missing dark matter is has been solved by the research. There is no empty space in the universe. The intergalactic space is filled with dark matter."
  5. It's not counterintuitive, it's incorrect. 'Empty' space has mass which is displaced by the particles of matter which exist in it and move through it. In a double slit experiment it is the dark mass that waves. The 60 atoms always exist as a C60 molecule. In a double slit experiment the C60 molecule, all 60 atoms, travels a well defined path which takes it through a single slit. It is the associated wave in the dark mass which passes through all of the slits.
  6. Wave-particle duality is a moving particle and its associated wave in the dark mass. In a double slit experiment the particle travels through a single slit and the associated wave in the dark mass passes through both, analogous to a boat double slit experiment where the boat travels through a single slit and the bow wave passes through both.
  7. How can I 'prove' the particle always detected traveling through a single slit in a double slit experiment is evidence the particle always travels through a single slit? If you insist on not understanding the boat always detected traveling through a single slit is evidence the boat always travels through a single slit there is no amount of evidence that will convince you otherwise. If you insist the bow wave moves with the boat as a clump of stuff analogous to how the steering wheel moves with the boat there is no amount of evidence which will convince you that boats move through and displace the water. The boat always detected traveling through a single slit in a boat double slit experiment is the evidence the boat always travels through a single slit. The particle always detected traveling through a single slit in a double slit experiment is the evidence the particle always travels through a single slit. The wave of wave-particle duality is a wave in the mass which fills 'empty' space. If you insist the boat and its bow wave are a single entity moving through an empty void as a clump of stuff there is no amount of evidence which can convince you otherwise.
  8. The notion that 60 atoms are each traveling every possible path then form a C60 molecule upon detection is utter nonsense. The C60 molecule is a particle which has an associated wave in the dark mass. The C60 molecule is always a particle which has an associated wave. You would not expect to measure the molecule exiting both slits because the molecule always travels through a single slit,. Wave-particle duality is a moving particle AND its associated wave in the dark mass. Particles are particles and waves are waves. Mathematics does not describe what is occurring physically in nature. 'Quantum mechanics rule 'bent' in classic experiment' http://www.bbc.co.uk/news/science-environment-13626587 'For his part, Professor Steinberg believes that the result reduces a limitation not on quantum physics but on physicists themselves. "I feel like we're starting to pull back a veil on what nature really is," he said. "The trouble with quantum mechanics is that while we've learned to calculate the outcomes of all sorts of experiments, we've lost much of our ability to describe what is really happening in any natural language. I think that this has really hampered our ability to make progress, to come up with new ideas and see intuitively how new systems ought to behave."' A moving particle has an associated wave in the dark mass. In a double slit experiment the particle travels through a single slit. It is the associated wave which passes through both. As the wave exits the slits it creates wave interference. As the particle exits a single slit the direction it travels is altered by the wave interference. This is the wave guiding the particle. Strongly detecting the particle causes a loss of cohesion between the particle and its associated wave, the particle continues on the trajectory it was traveling and it does not form an interference pattern. What waves in a double slit experiment is the dark mass. 'Dark matter' is now understood to fill what would otherwise be considered to be empty space. 'Cosmologists at Penn Weigh Cosmic Filaments and Voids' http://www.upenn.edu/pennnews/news/c...ents-and-voids "Dark matter ... permeate all the way to the center of the voids." 'No Empty Space in the Universe --Dark Matter Discovered to Fill Intergalactic Space' http://www.dailygalaxy.com/my_weblog...ic-space-.html "A long standing mystery on where the missing dark matter is has been solved by the research. There is no empty space in the universe. The intergalactic space is filled with dark matter." 'Empty' space has mass and is what waves in a double slit experiment.
  9. 'Dark matter' is now understood to fill what would otherwise be considered to be empty space. 'Cosmologists at Penn Weigh Cosmic Filaments and Voids' http://www.upenn.edu/pennnews/news/cosmologists-penn-weigh-cosmic-filaments-and-voids "Dark matter ... permeate all the way to the center of the voids." 'No Empty Space in the Universe --Dark Matter Discovered to Fill Intergalactic Space' http://www.dailygalaxy.com/my_weblog/2012/02/no-empty-space-in-the-universe-dark-matter-discovered-to-fill-intergalactic-space-.html "A long standing mystery on where the missing dark matter is has been solved by the research. There is no empty space in the universe. The intergalactic space is filled with dark matter." I use the term 'dark mass' to describe the mass which fills 'empty' space. Particles of matter move through and displace the dark mass, including 'particles' as large as galaxies and galaxy clusters. In the following two articles the aether is what waves in a double slit experiment. In the first article the aether has mass. In other words, it is the dark mass that waves in a double slit experiment. 'From the Newton's laws to motions of the fluid and superfluid vacuum: vortex tubes, rings, and others' http://arxiv.org/abs/1403.3900 "This medium, called also the aether, has mass and is populated by the particles of matter which exist in it and move through it" ... ... and displace it. 'EPR program: a local interpretation of QM' http://arxiv.org/abs/1412.5612 "Wave particle duality is described as the compound system of point particle plus accompanying wave (in the æther)." Q. Why is the particle always detected traveling through a single slit in a double slit experiment? A. The particle always travels through a single slit. It is the associated wave in the dark mass which passes through both. The wave of wave-particle duality is a wave in the dark mass. Here are some articles where the observed physical phenomenon is correctly described by the matter moving through and displacing the dark mass. 'Galactic Pile-Up May Point to Mysterious New Dark Force in the Universe' http://www.wired.com/wiredscience/2013/01/musket-ball-dark-force/ "The reason this is strange is that dark matter is thought to barely interact with itself. The dark matter should just coast through itself and move at the same speed as the hardly interacting galaxies. Instead, it looks like the dark matter is crashing into something  perhaps itself – and slowing down faster than the galaxies are. But this would require the dark matter to be able to interact with itself in a completely new an unexpected way, a “dark force†that affects only dark matter." It's not a new force. It's the dark mass displaced by each of the galaxy clusters interacting analogous to the bow waves of two boats which pass by each other. 'The Milky Way's dark matter halo appears to be lopsided' http://arxiv.org/abs/0903.3802 "the emerging picture of the dark matter halo of the Milky Way is dominantly lopsided in nature." The Milky Way's halo is not a clump of dark matter traveling along with the Milky Way. The Milky Way's halo is lopsided due to the matter in the Milky Way moving through and displacing the dark mass. 'Offset between dark matter and ordinary matter: evidence from a sample of 38 lensing clusters of galaxies' http://arxiv.org/abs/1004.1475 "Our data strongly support the idea that the gravitational potential in clusters is mainly due to a non-baryonic fluid, and any exotic field in gravitational theory must resemble that of CDM fields very closely." The offset is due to the galaxy clusters moving through and displacing the dark mass. The analogy is a submarine moving through the water. You are under water. Two miles away from you are many lights. Moving between you and the lights one mile away is a submarine. The submarine displaces the water. The state of displacement of the water causes the center of the lensing of the light propagating through the water to be offset from the center of the submarine itself. The offset between the center of the lensing of the light propagating through the water displaced by the submarine and the center of the submarine itself is going to remain the same as the submarine moves through the water. The submarine continually displaces different regions of the water. The state of the water connected to and neighboring the submarine remains the same as the submarine moves through the water even though it is not the same water the submarine continually displaces. This is what is occurring as the galaxy clusters move through and displace the dark mass. 'Hubble Finds Ghostly Ring of Dark Matter' http://www.nasa.gov/mission_pages/hubble/news/dark_matter_ring_feature.html "Astronomers using NASA's Hubble Space Telescope got a first-hand view of how dark matter behaves during a titanic collision between two galaxy clusters. The wreck created a ripple of dark matter, which is somewhat similar to a ripple formed in a pond when a rock hits the water." The 'pond' consists of dark mass. The galaxy clusters are moving through and displacing the dark mass. The ripple created when galaxy clusters collide is a wave in the dark mass. What ripples when galaxy clusters collide is what waves in a double slit experiment; the dark mass. Einstein's gravitational wave is de Broglie's wave of wave-particle duality; both are waves in the dark mass. Dark mass displaced by matter relates general relativity and quantum mechanics. - - - Updated - - - Someone posts that I have not provided any evidence that 'empty' space has mass. Then I post an article which says, "There is no empty space in the universe. The intergalactic space is filled with dark matter.". Then someone posts that I have not provided any evidence that 'empty' space has mass. Then I post an article which says, "There is no empty space in the universe. The intergalactic space is filled with dark matter.". ... And on and on it goes all in order so people don't have to correctly understand what occurs physically in nature. You are able to understand in a boat double slit experiment the boat travels through a single slit and the bow wave passes through both, correct? 'Empty' space has mass which is displaced by the particles of matter which exist in it and move through it. The wave of wave-particle duality is a wave in the mass which fills 'empty' space. Do you know why the particle is always detected traveling through a single slit in a double slit experiment? Because it always travels through a single slit.
  10. All mainstream physics has to do is understand 'empty' space has mass which is displaced by the particles of matter which exist in it and move through it and the nonsense associated with it is corrected.
  11. Complete nonsense. Double slit experiments have been.performed with C60 molecules, that's 60 interconnected atoms. Are you telling me there are 120 atoms physically travelling through both slits and only 60 are detected exiting a single slit? Are you telling me 40 atoms travel through one slit and 20 through the other and when it interacts with the detector it is a single molecule again? Just saying 'wavefunction collapse' does not explain what is occurring PHYSICALLY in nature. When a double slit experiment is performed with a C60 molecule the molecule travels through a single slit. It is the associated wave in the dark mass which passes through all of the slits. - - - Updated - - - Come back when you can explain how it is the particle exits both slits and is only detected by one of the detectors. Come back when you can explain how when a double slit experiment is performed with a C60 molecule, and according to you the C60 molecule passes through all of the slits, that when there are detectors at the exits to the slits all 60 atoms are always detected exiting a single slit and none exit the other. In a double slit experiment, the particle travels a well defined path which takes it through one slit and the associated wave in the dark mass passes through all of the slits.
  12. So, now the particle physically travels through both slits, exits both slits and is only detected exiting a single slit? All this nonsense in order to not understand wave-particle duality is a moving particle and it's associated wave.
  13. If the particle physically travels through both slits it would be detected exiting both slits. In every double slit experiment ever performed where detectors are placed at the exits to the slits the particle is always detected exiting a single slit. This is evidence the particle always travels through a single slit. In a double slit experiment the particle travels through a single slit and the associated wave in the dark mass passes through both.
  14. That's called weak measurement. '1st place: Shifting the morals of quantum measurement' http://physicsworld.com/cws/article/news/2011/dec/16/physics-world-reveals-its-top-10-breakthroughs-for-2011 "Using an emerging technique called "weak measurement", the team is the first to track the average paths of single photons passing through a Young's double-slit experiment – something that Steinberg says physicists had been "brainwashed" into thinking is impossible." 'Quantum mechanics rule 'bent' in classic experiment' http://www.bbc.co.uk/news/science-environment-13626587 'For his part, Professor Steinberg believes that the result reduces a limitation not on quantum physics but on physicists themselves. "I feel like we're starting to pull back a veil on what nature really is," he said. "The trouble with quantum mechanics is that while we've learned to calculate the outcomes of all sorts of experiments, we've lost much of our ability to describe what is really happening in any natural language. I think that this has really hampered our ability to make progress, to come up with new ideas and see intuitively how new systems ought to behave."' 'New 'Double Slit' Experiment Skirts Uncertainty Principle' http://www.scientificamerican.com/article.cfm?id=new-double-slit-experiment-skirts-uncertainty-principle "Intriguingly, the trajectories closely match those predicted by an unconventional interpretation of quantum mechanics known as pilot-wave theory, in which each particle has a well-defined trajectory that takes it through one slit while the associated wave passes through both slits." The following is what is incorrect in quantum mechanics. "David Deutsch of the University of Oxford, UK, is not convinced that the experiment has told us anything new about how the universe works. He says that although "it's quite cool to see strange predictions verified", the results could have been obtained simply by "calculating them using a computer and the equations of quantum mechanics". ... " Yes, you can obtain the results by "calculating them using a computer", however, that doesn't explain what is occurring physically in nature. " ... "Experiments are only relevant in science when they are crucial tests between at least two good explanatory theories," Deutsch says. "Here, there was only one, namely that the equations of quantum mechanics really do describe reality."" Equations do not describe what is occurring physically in reality. A moving particle has an associated wave in the dark mass. In a double slit experiment the particle travels through a single slit. It is the associated wave which passes through both. As the wave exits the slits it creates wave interference. As the particle exits a single slit the direction it travels is altered by the wave interference. This is the wave guiding the particle. Strongly detecting the particle causes a loss of cohesion between the particle and its associated wave, the particle continues on the trajectory it was traveling and it does not form an interference pattern. Weakly detecting the particle allows for the particle and its associated wave to maintain some of their cohesion, allowing the particle to still form an interference pattern. What waves in a double slit experiment is the dark mass.
  15. The following is incorrect: "The effect is called "gravitational lensing" and it can be used to figure out where the clouds of dark matter are." There are no such things as "clouds of dark matter". 'Empty' space has mass which is displaced by the particles of matter which exist in it and move through it. What is mistaken for the "clouds of dark matter" is the state of displacement of the dark matter, analogous to a submarine moving through and displacing the water. The following is incorrect: "The first way is to observe dark matter in action in the cosmos." The first way to 'observe' dark matter is in a double slit experiment, it's what waves. In a double slit experiment the particle travels through a single slit and the associated wave in the dark matter passes through both. "These make intricate patterns known as the "cosmic web". This web is tied together with dark matter." The web is the state of displacement of the dark matter. The galaxy clusters are moving through and displacing the dark matter.
  16. Not one of those quotes says the particle goes through both slits simultaneously. If it did you would detect the particle in both slits. They all talk about the sum of the paths. They do this because mainstream physics is too screwed up to realize there is a particle AND a wave. Email your favorite physics professor and ask them if the particle physically travels through both slits simultaneously in a double slit experiment. The answer will be 'no'. You are mistaking the sum of the paths, which is nonsense in its own right, with the particle physically traveling through both slits. If you do not want to correctly understand what occurs physically in nature then that is your choice. In a double slit experiment the particle travels through a single slit and the associated wave passes through both.
  17. No one thinks the particle travels through both slits. Some say it exists in all of configuration space. There is the nonsense of many worlds. The Copenhagen Interpretation says it is meaningless to discuss where the particle is prior to detection. Only you say the particle travels through both slits. If it did you would detect it in both.
  18. If the particle passed through both slits it would be detected in both slits. Double slit experiments have been performed with C60 molecules. That's 60 interconnected atoms. If it passed through both slits atoms would be detected in both slits. That doesn't happen. The C60 molecule is always detected as a single entity, all 60 atoms, because it is always a single particle. It is the associated wave in the dark mass that passes through all of the slits.
  19. Bell's inequality has to do with hidden variables. I recommend watching all of the following video. The part having to do with 'exposed variable theories' is at the 2:10 mark. 'The pilot-wave dynamics of walking droplets' Due to conservation of momentum the downconverted pair are propagating with opposite angular momentums. Each of the pair is able to determine the position and momentum of the other based upon their own position and momentum. Entanglement is each of the pair being able to determine the state of the other. de Broglie's double solution theory is an exposed variable theory. 'Empty' space has mass which is displaced by the particles of matter which exist in it and move through it. In a double slit experiment it is the mass which fills 'empty' space that waves. The wave of wave-particle duality is a wave in the mass that fills 'empty' space.
  20. Or, you could understand the particle always detected traveling through a single slit in a double slit experiment is evidence the particle always travels through a single slit. You do understand in a boat double slit experiment the boat travels through a single slit even when you close your eyes, correct? There is a boat AND a bow wave. It's that simple for wave-particle duality. There is a particle AND a wave in the mass which fills 'empty' space. It doesn't matter how much evidence there is that boats move through and displace the water if you insist on not understanding boats move through and displace the water. It doesn't matter how much evidence there is that wave-particle duality is a moving particle and it's associated wave if you insist on not understanding a moving particle has an associated wave in the mass which fills 'empty' space. Do you need to see a derivation of the bow wave to understand boats move through and displace the water?
  21. I'm not discussing de Broglie-Bohm pilot wave mechanics. I am discussing de Broglie's double solution theory. de Broglie-Bohm theory is incorrectly named as de Broglie disagreed with it. It should be called Bohmian mechanics. NON-LINEAR WAVE MECHANICS A CAUSAL INTERPRETATION by LOUIS DE BROGLIE "During the summer of 1951, there came to my attention, much to my surprise, a paper by David Bohm which appeared subsequently in The Physical Review [3]. In this paper Bohm went back to my theory of the pilot-wave, considering the W wave as a physical reality* He made a certain number of interesting remarks on the subject, and in particular, he indicated the broad outline of a theory of measurement that seemed to answer the objections Pauli had made to my approach in 1927.3 My first reaction on reading Bohm’s work was to reiterate, in a communication to the Comptes rendus de VAcademic des Sciences [4], the objections, insurmountable in my opinion, that seemed to render impossible any attribution of physical reality to the W wave, and consequently, to render impossible the adoption of the pilot-wave theory." In the following de Broglie is agreeing with Bohm (and Vigier) in terms of the wave of wave-particle duality being a wave in a "subquantic medium". “Since 1954, when this passage was written, I have come to support wholeheartedly an hypothesis proposed by Bohm and Vigier. According to this hypothesis, the random perturbations to which the particle would be constantly subjected, and which would have the probability of presence in terms of W, arise from the interaction of the particle with a “subquantic medium†which escapes our observation and is entirely chaotic, and which is everywhere present in what we call “empty spaceâ€Â.†How you are able to interpret "subquantic medium" as not being a medium is beyond comprehension. I recommend watching all of the following video. The part having to do with 'exposed variable theories' is at the 2:10 mark. 'The pilot-wave dynamics of walking droplets' Due to conservation of momentum the downconverted pair are propagating with opposite angular momentums. Each of the pair is able to determine the position and momentum of the other based upon their own position and momentum. Entanglement is each of the pair being able to determine the state of the other. de Broglie's double solution theory is an exposed variable theory. 'Empty' space has mass which is displaced by the particles of matter which exist in it and move through it. In a double slit experiment it is the mass which fills 'empty' space that waves. The wave of wave-particle duality is a wave in the mass that fills 'empty' space.
  22. NON-LINEAR WAVE MECHANICS A CAUSAL INTERPRETATION by LOUIS DE BROGLIE “Since 1954, when this passage was written, I have come to support wholeheartedly an hypothesis proposed by Bohm and Vigier. According to this hypothesis, the random perturbations to which the particle would be constantly subjected, and which would have the probability of presence in terms of W, arise from the interaction of the particle with a “subquantic medium†which escapes our observation and is entirely chaotic, and which is everywhere present in what we call “empty spaceâ€Â.†The “subquantic medium†is the dark mass. ‘Fluid mechanics suggests alternative to quantum orthodoxy’ http://newsoffice.mit.edu/2014/fluid-systems-quantum-mechanics-0912 “The fluidic pilot-wave system is also chaotic. It’s impossible to measure a bouncing droplet’s position accurately enough to predict its trajectory very far into the future. But in a recent series of papers, Bush, MIT professor of applied mathematics Ruben Rosales, and graduate students Anand Oza and Dan Harris applied their pilot-wave theory to show how chaotic pilot-wave dynamics leads to the quantumlike statistics observed in their experiments.†A “fluidic pilot-wave system†is the dark mass. ‘When Fluid Dynamics Mimic Quantum Mechanics’ http://www.sciencedaily.com/releases/2013/07/130729111934.htm “If you have a system that is deterministic and is what we call in the business ‘chaotic,’ or sensitive to initial conditions, sensitive to perturbations, then it can behave probabilistically,†Milewski continues. “Experiments like this weren’t available to the giants of quantum mechanics. They also didn’t know anything about chaos. Suppose these guys  who were puzzled by why the world behaves in this strange probabilistic way  actually had access to experiments like this and had the knowledge of chaos, would they have come up with an equivalent, deterministic theory of quantum mechanics, which is not the current one? That’s what I find exciting from the quantum perspective.†What waves in a double slit experiment is the dark mass.
  23. It has everything to do with how it got there. Wave-particle duality is a moving particle AND it's associated wave in the dark mass. The particle is always detected traveling through a single slit because it ALWAYS travels through a single slit. It is the associated wave in the dark mass that passes through both.
  24. Wave-particle duality is a moving particle AND it's associated wave in the dark mass.
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