The Double-Slit Experiment

By John Dobson
Published 2004-10-22 13:05:52
From 1996
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Richard Feynman has pointed out that every statement in quantum mechanics is a restatement of Heisenberg' uncertainty principle. Now Heisenberg's uncertainty principle states that the product of our uncertainty in the position of a particle and our uncertainty in its momentum can never be less than a certain small quantity, namely Planck's constant over two pi. Also that our uncertainty in the energy of a particle and our uncertainty in when it has that energy can never be less than that same small amount.

Feynman has also pointed out that the entire mystery of quantum mechanics is in the double-slit experiment. And that is what makes it so very interesting. From the standpoint of common sense, as Feynman himself has pointed out, the behavior of Nature is absurd. And this absurdity is nowhere more obvious than in the double-slit experiment. But before we discuss the double-slit experiment, let us go back to Einstein's 1905 geometry.

Euclid's geometry is a theoretical geometry about a theoretical space that does not in fact exist. And Newton's physics is a theoretical physics about a theoretical world that does not in fact exist. So we have had to change all that with relativity and quantum mechanics. In 1905 Einstein succeeded in putting time into geometry where it belongs. He changed our geometry form 3-D to 4-D. and in Pythagoras' theorem for four dimensions, time comes in squared with a minus sign, so that if the space and time separations between two events are equal, the total space-time separation between them is zero. Distances in space are not objective, nor are lengths of time. Observers moving with respect to each other may disagree on how far it is from there to here and on how long it took from then till now, but they will all agree on the total space-time separation between there-then and here-now. Four-dimensional addresses (where and when) are objective, and the space-time intervals between them are also objective, regardless of your position or your state of motion.

Now in discussing the double-slit experiment, it will be important to remember what happened to our geometry in 1905. Space and time come into that geometry as a pair of opposites. And since, between the emission and the absorption events of a single photon, the time separation as always equal to the space separation (for all observers), the total separation between those two events must always be zero. When Einstein threw out the luminiferous ether, he should have thrown out the photons that moved in it. They do not show up in his physics. When he threw out the lake, he should have thrown out the fish that swam in it.

The mystery of the double-slit experiment is this: that if the photons go one at a time through the slits, how do they know that both slits are open?

From a little distance away we shoot a laser through two closely spaced slits and watch the absorption events on a scintillating screen behind the slits. What we see is that when one slit is closed, most of the scintillation points fall behind the other slit, as we would expect. But when both slits are open, most of the scintillation points fall not behind the two slits, as we would expect, but between them. It is as though the photons had come through as waves and showed an interference pattern on the screen. And the question is this: since photons come through one at a time, how do they know that both slits are open?

It will be necessary here to remember that space and time are a pair of opposites and that the total separation between the emission and absorption events are adjacent in space-time. Now the adjacency has two components, a space component and a time component, and it is in the space component of the adjacency that both slits are open. It is not that the photons go through one or the other slit, but only that the space components of the trajectories have both slits open.

But suppose we do the double-slit experiment with electrons instead of photons. Then the emission and absorption events will not be adjacent in space-time, because the electrons can't travel at the speed of light. And then the space and time components of the trajectories will not be equal. What the? Still we get the same result. If both slits are open, we get interference on the screen behind the slits. Why? Because even if the space and time components fo the trajectories are not equal, still both slits are open for the space components.

As Amit Goswami says, "We never, never see the wave aspect of a single quantum object." The wave aspect is in the space component of the trajectory.

Feynman's "sum-over-histories" approach suggests that we must allow that the photon (or the electron) could have gone by any possible way from the laser (or the electron gun) to the screen, and we sum-over-the-histories to calculate the probability of its arrival. Actually what we do is to sum-over-the-space-components-of-the-trajectories, whether for a photon or an electron.

For a detailed description of the double-slit experiment please see Richard Feynman's Six Easy Pieces. It's in the last chapter on Quantum Behavior.

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• By M. De Zayas on 2005-06-27 13:24:29
  “The young Experiment: the untold story” Never before in the history of humanity the concepts of human intuition, logic and common sense have been regarded as an unfortunate “liability” rather than a blessing. The “metamorphosis” observed since the last hundred years in the field of science, especially theoretical physics and philosophy, have put humankind’s intellectual abilities to the test. Randomness and uncertainty have become part of our own reality ever since. The subject of this article as its title anticipates is about “The Two Slits Experiment.” I think that it’s not necessary for neither of us repeating the set-up of the experiment and its final conclusions as it has been performed countless times in every physicist’s laboratory around the world. The aim of my story is to prove that there are “hidden variables” as Einstein used to refer in the past in regard to the “weird” nature of Quantum Mechanics. “God never played dice as he wisely said… We did.” I will have to use a little bit of “magic” if you will… I will ask you to open your mind to an “alternate reality” in other words; I will describe to you how a sci-fi writer would explain the conclusive results so well documented by experimentalists during the so-controversially famous two hundred years old experiment with light. The only condition I will ask from you is to relax and, at least for the duration of these readings, put aside all sorts of mathematical equations and spatial geometric “snacks.” Great! Before we start though I need to introduce you with some necessary concepts we will see in their entirely new reformulation… It’s a completely different universe, remember? Let’s start first with the difference between mass and matter. In “my universe” mass is described as “infinitesimally small specks of “dust,” so tiny that we can’t see them at all. We had to wait until energy popped into the equation to “make it visible.” I guess we may call it “Dark Matter” but to be honest with you I preferred to call it “Dark Mass” instead. What is matter then? Now this is the tricky part! If you thought that mass was the only one with the rights to be so tiny you were wrong this time too. Energy is in our alternate universe as infinitesimally small as dust could be since both were the result of a terrible explosion that occurred with the genesis of our universe. After the “Big-Bang” those little specks of tiny radiation energy began to interact with each other following a process of integration as more and more tiny specks of energy became part of the fusion. There is a new theory that explains this integration of “point-energies” in space; the name of the theory is “String Theory.” Well, they see those interactions as “strings” or vibrations of energies in a bunch of spatial dimensions that I lost count, but I’ll tell you a secret: those “vibrations” in space are nothing more than “Standing Nuclear Waves.” … What did I just say? I know… another new crazy concept! The smallest piece of matter in the universe is called “atom.” –“Wait a minute alligator! Our books make references to “sub-atomic particles with names like quarks, protons, neutrons and electrons among many others, are they matter too?”- No! But this will take more of your time to explain. What is an atom? It couldn’t be simpler I promise. The atom is a result of many of those specks of energy we talked about before in a complex structure of mutual integration. The only way energy guarantees its “survival” which also means its perpetuity in its lowest possible state is achieving a pattern of “Standing Waves.” Do you need a better proof of that statement that sound waves inside a room? Our universe is a fairly big “room” with no walls or physical boundaries we know about, but the existence of energy in it depends on its own ability to reach a perfect symmetry. Let’s continue with our atom and its “internal anatomy.” We all know the pattern of interference called “standing waves.” The process that takes place at the core of the atom is ultimately responsible for the presence of harmonic levels of energy spinning around it. If you could imagine in your mind a complex pattern of elliptical standing waves overlapping among each other I bet it would be pretty easy for you to come across the image of a “string”… Was that too difficult to picture inside your mind? I guess not! Before we get to that point I have a very important question to ask you: Is the perfect vacuum possible in our universe? I hope that your answer was “NO” and we all agree on that. Are evidences to support such statement required in this case? No problem! Have we ever reached the absolute temperature of 0 Kelvin? I tell you why not in a moment. At that low temperature free energy is zero, which means that there is absolutely no energy in that spot of space. I want you to take my word for granted when I say that there is nothing in this universe that prevent energy from moving from one point to the other. There is no “barrier” or obstacle of any kind that could stop thermodynamic energy from spreading across space. Why is that so important in this discussion about the atom? Simple! The atom is permeated by heat from the surroundings and that heat share with mass (dust remember?) the “empty space” across those spinning patterns we spoke before. What was that all about…? Open you mind because I will share with you the greatest secret of all! As those patterns of “Standing Nuclear Waves” spin around confronting specks of radiation, energy in the form of waves cancel each other off as they complete their momentum. At the very point in space where mutually interfering energy waves cancel each other off a perfect vacuum is about to “open” a breach in the universal law that defines a proportional density energy-mass at that specific point in space. In the rescue of that density violation, mass rush to the scene from the vacuum and takes its place inside the atom. Now we have a proportional amount of mass spinning around inside a pattern created by confronting energies. We also have a multi-level structure of harmonics known by physicists as orbital following the familiar “Standing Wave” pattern known to us in music. I don’t know about you but the whole thing start looking more and more like the atom we see in our observations. What comes next is the trickiest thing of all! “The nature of time.” Since this is a story, told by a sci-fi writer with no evidence of what he is saying other than the help He could get from your own intuition and common sense, I will ask you to use all your imagination and concentration in picturing what I’m about to say. Time, in other words, the absolute elapsing rate of time across the atom is not uniform. It changes from one harmonic to the next. The concept is difficult to grasp but it is essential in the understanding of puzzles you can’t even imagine so far, so I beg you to do an effort and try to stay with me for a while. Imagine a horse race. The center of the tracks would be the core of our atom, no big deal. The track closer to the core (horse number one) will run at a lower speed absolute speed than horse number two and so on. As in the weirdest scenario ever, you would be sitting in front of a bunch of horses running in different realities. More like a film made to run in different speed for each horse… too alien I guess! Imagine this! For horse number four the one to its left (horse number three) was running at a lower-speed-reality while to its right (horse number five) was moving faster at an impossible-to-believe-speed. If you could talk to the man running on top of horse number four and asked him about his impressions, He would probably say that time was going backward for horse number three while otherwise time was moving forward for horse number five. Inside of every single atom there is a “track for horse number four.” We call it “the center of mass.” The same place we located our “protons.” Everything closer to the core of the atom seems like moving in an image of our world. Time looks like moving “backwards” although it moves forward too. It’s all a matter of relativism. However, the actual passage of time is different, there was nothing purely relative about it at all. Time does change its elapsing speed as we move from one orbit to the next. Now we can say that we have a better picture of the real atom that makes every piece of matter in my alternate universe. Q. –“If protons, neutrons and electrons were patterns inside the atom with a magnitude of dust spinning around it in a complex time structure, how do you defined electrons “outside the atom then?” A. Good question! We know that atoms have the ability to absorb radiation energy, transforming it (modulating it) into a different quantum and scattering it later. How that happened in our new atomic model? As soon as energy is “absorb” mass is pushed to the outermost orbits of the atom once its presence is no longer required. As you may recall, the tiny specks of mass were necessary to fill the “blanks” left behind two canceling waves in space, with the new energy absorbed inside, mass was scattered back to the vacuum. Not for too long though! After the newly produced quantum leaves the atom to start traveling across space with the name of “photon” mass rush back into the spin “by express order given by the universe.” The process of manufacture of an electron is somewhat more complicated than the case of the photon since the presence of two or more atoms are required. Electrons “outside the atom” are also “modulated” by what you have called “atomic oscillators” in some books (my harmonics). The tricky thing is that producing electrons require a “specific misalignment” and/or and uncompensated pattern at the outermost orbital of the atoms involved in those molecules. The answer to the phenomenon called “tunneling” is lying inside this concept-model. I believe that we have given to you a “crash course” into the internal mechanics of the atom in my universe. Before I explain the mystery hidden in the two-slit experiment, I must talk a little bit about the force of gravity and its secret nature. Gravity, in my weird universe, is not the consequence of space-time “warped” by the sole presence of mass. In my universe gravity is a prerogative of stars. The sun of my planet (we call it Earth too) irradiate what we call “Gravitational Waves” that move planets around the star. Those affluent solar waves resemble trochoidal waves observed in ocean waves. The arrival of those huge waves to our “shores” (the surface of our planet) moves Earth and the other planets around the sun and moons around their home planets. Mass or matter as we know it is inert and do not exert any force of any kind on other bodies. Using some philosophy of sci-fi worlds, “Reality is the result of the rate of interaction between solar gravity waves and it is edited accordingly.” Time however behaves at the scale of solar systems much like inside the atoms. The absolute elapsing rate of time in each planetarium orbit of our solar system is different from each other. One good reason why planets can’t collide among each other and comets “ignore” the “huge space-time warp” we believe exist around “big masses.” Do you want to know why you have a pile of junk on the surface of Mars? Time is responsible for that too! But let’s go back to the topic of this article, “The Young experiment.” Using high energy-light the process could be depicted the following way: A light-wave is projected across the two slits according to the set-up of the experiment. The physically existent light-wave travel across both slits interacts with itself and hits a spot in the screen. “Y” or the controversially popular mathematical “life-saver” we call “wave-function” was no other than our (real) light wave. A quantum, gentlemen, is energy (a defined quantity I agree) but nothing more than energy. Energy obeys only one rule: “The law of conservation of itself.” That’s it! It could go through two or hundred “holes or slits” as many as you wanted to open, but “at the end of the day” the multiple pieces “collapse” into one and the same quantum originally “split.” If you are worry thinking about the mass of your little “particle,” don’t! There is plenty in the vacuum to chose from, the universe takes care of it… I assure you that! That’s why I found very funny the “law of conservation of mass.” It’s just an image of the real one. Q-“Ok, but what about the defined pattern or spectrum? Nothing you had said so far explains it. We have shot one photon at a time and we still keep getting the same results… How about that?” A. Right! What’s missing here? Oh yes! The Ether! The only reason a bunch of cloned-photons hit a different spot in the screen but still keeps the pattern of bright and dark fringes on the screen is due to the existence of the Ether. The interaction between those affluent gravitational waves from the sun coming to the Earth’s surface and the mutual interaction with our light-wave determined the final position of the blotch on the screen, we are talking about two different scales interacting with each other. Without those “solar waves” responsible for gravity there would be no light at all. The needed “feedback” for our photon is guaranteed by those waves that are part of the vacuum we hardly understand anymore. Once the photon hits the screen the energy makes a lighting spot “collapsing” our real wave into out time frame. Remember Russell’s “solitary waves”? Now, my dear friend. Do you still consider necessary to repeat the same explanation using a dimmer light? Do you really think it would make a difference in our final arguments and conclusions? I guess you should go back to your lab and try a crazy idea coming from another crazy sci-fi writer whose being kidnapped by aliens… That’s what I think. The reason of our uncertainty is given by the fact that we don’t understand the nature of the vacuum around us. We don’t understand the relationship between mass and the energy wave while propagating throughout space. Is light a particle? To answer that question I would have to ask you this: what is a particle for you? A quantum (specific magnitude of energy) with a defined magnitude of mass proportional to the rate of wave cancellation during its own propagation? Is that “your particle” Sr.? I fail to see your point! We agree on the “bundle” of energy scattered from an atom during our exposition. Nobody has ever said that energy is a continuous “thing” with no end! Energy propagates in a wave-format and that’s a fact. The propagation carries in itself the concept of moving energy in a permanent transformation, so mass must guarantee that process preventing the creation of a perfect vacuum. I apologize for my lack of vision on this subject, but where was your particle in all this? You can’t even locate your electrons around your atom for God’s sake, you can’t detect the mass between detectors for obvious reasons I may add, so how could you expect me to believe that there is a “duality” and a paradox with respect to the conclusions of the experiment? If Einstein himself didn’t rush to exile Maxwell’s ether from our scientific literature in 1905 you wouldn’t be embarrassed today over assumed incongruent conflicts between waves and particles. So stop arguing against human intuition, logic and common sense and let’s do physics! I believe I came up with ways to demonstrate my point, after all: We must set-up the “two slits experiment” once again but this time we must do it right! If my predictions are right we should see a “quantifiable displacement” of the spectrum of bright and dark bands to either side of the screen under the following conditions: 1) In the lapse of 24 hours. 2) Between the different phases of the moon. 3) Between summer and winter. 4) Also if we repeat the experiment under extreme pressure and temperature conditions other than room temperature. Because by changing the specific “free energy” or internal energy of the atoms involved in the generation of quanta (photons or electrons) components of the “emitter” we begin producing different conditions for “feedback” from the Ether altering the spectrum. How could you explain superconductivity in certain materials subject to extremely low temperatures? By lowering the “internal thermodynamic energy” present in those atoms you are “forcing the universe” to take extreme measures by ordering mass to get its “ass” inside the pattern of “Standing Nuclear Waves” and change as a result the lattice structure. You could compare with a scanning tunneling microscope or other ways at your disposals that the final “visible mass” of the super-conducting material has increased with respect to lower temperatures, can’t you? An internal rearrangement (for good) in the structure of those couplings (molecular bonding as you know it) produces the right conditions for the rejection of external flux of magnetic fields, “The Meissner Effect.” If under the new conditions more mass is now present in the atomic oscillator, we have raised its “modulating capacity” to a higher level, haven’t we? We would be able then to “manufacture” two twin electrons instead of just one… “The cooper pairs” see BCS theory. Increasing the external pressure does the same results as lowering the temperature according to the laws of thermodynamics: making “mad” the universe and changing the magnitude of mass making it visible or invisible according to the established universal density. LASER in my universe is not explained by the so-called “population inversion” of electrons jumping up and down either. The phenomenon in my alternate universe was explained by a stimulated “collapse of entanglement” of scattered photons. In my world, we didn’t have to use what you call “trial and error” to select the right materials for lasers. We understand the vacuum and we can determine what photons are considered “legitimate” which also means which ones are allowed to be scattered by a number of atomic orbits. The universe instantaneously does the selective process by “filtering” those quanta that will not match its signature with the solar waves. “Feedback” is an essential pre-condition in the final selection, if it is not present, the atom won’t bother scattering a defect photon, instead it will wait for the next lower orbit to be included in the process. That’s the reason why some scattering take longer to occur in some atoms like in phosphorus during phosphorescence. The time dilation is due to the different elapsing rate of time between orbits, as I’ve just explained earlier. OOPS! My ship is about to leave orbit. I’ve got to go back to my galaxy now… these aliens are too serious! It’s been an honor having taken a look to your science. You know? Long time ago we were also pretty confused by that “duality thing” you are dealing today in your equations… It’ll go away, believe me! We are pure energy inside, mass is just a tool to guarantee our existence in the universe. At some point in the past this was common knowledge but it changed. We began to believe ourselves as made out of crunches of matter and a bunch of guys called reductionists have spent a lot of time and resources trying to find the smallest piece of that crunch. It took milleniums to realize how wrong we were then. I hope this little tip will make a difference. “To hell with the “prime directive!”. Author: Miguel De Zayas To learn more about my alternate universe you may go to: www.humanbydefault.com You all have a nice day!

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