question about spatial  - in quantum mechanics?
482358
I admire mathematician's concise answers, but in this case some additional explanation may be due:\n\nWhen a wave is partially transmitted and partially reflected the two outgoing waves are shifted in phase from the incident wave. If energy or probability is to be conserved, the difference between the two phase shifts is pi/2 (90°). In this diagram each of the two possible outgoing  beams consist of components from two paths (R=Reflection,T=Transmission):\n\nOutgoing Horizontal: TRR + RRT\nOutgoing Vertical: TRT + RRR\n\nIn the first case the relative phase shift between the two components is 0 and in the second case it's pi (180°) ==> the two components are negatives of each other and interfere destructively.
427866
>we know that physically one photon can not pass through the two slits at a time\n\nThat's kind of the whole point of considering the single photon case of the double slit experiment: it give results that don't match classical predictions, and so it becomes a good argument for quantum mechanics.  \n\nIf light were a classical particle, then yes, it can't go through both slits, and you'd end up with two overlapping Gaussian bands of light, and not an interference pattern if you summed up the results of many single photon experiments \n\nIf light were a classical wave, you'd get an interference pattern, but you'd expect the energy from it to be spread out all over the detector or photographic plate, just very faint.  \n\nWhat actually happens when this experiment is done is that the energy gets delivered to the detector all in one place, as if light is a classical particle.  But, the locations where the energy gets delivered, if the experiment is done one photon at a time and the results are stacked up, conforms to the interference pattern you'd expect from a classical wave.\n\nSo, we have something that matches neither a classical particle nor a classical wave in  behaviour.  \n\nBut, in quantum mechanics we have a description of something that does fit this behaviour.  That is, we have a wave which, when measured, has to provide energy in quantized steps.  To get from the wavelike portion to the particlelike portion, we have to recognize that there isn't a completely deterministic answer but rather a statistical one.  So, while this model descibes what a real photon does in the double slit experiment, it can't predict the exact behaviour of a specific given photon.  As best we can tell so far, this isn't just a shortcoming of the theory, it's actually how physical reality operates.\n\n\nEdit:  Ramblingman, it can be done with either an electron beam or a photon beam.  Both will show the same sort of effect, but traveling electrons will have a much shorter wavelength than light.  Quantum mechanics works for both things that were classically considered as waves, like photons, and things that were classically considered as particles, like electrons.
1046533
The first website gives a good overview with no math, if you already understand light/waves/atoms skip to the part that I put in paranthesis.\nThe third site is a more advanced and goes more into the consequences.  In case we have different ideas of what laymen are.\nHere's a quick summary:\nquantum entanglement is when one photon of light is split into two equal photons of opposite polarity (direction of the wave disturbance) .  The two photons seem to be linked in a way that is currently innexplicable but demonstratable using interference patterns.  Which I hope you don't consider techno babble, but if you do, just ask what interference patterns are and I'll answer that, too.  That's a quick expanations of what's happening.\nUnless you mean why, the last site does a pretty good job of explaining that we don't really know, but we're trying pretty hard to figure it out.  There are many theories right now.  It'll go over a couple of them.(it's really an excellent paper.  I don't know what level of physics education you have, but it was perfect for me.I'm not a physicist, I'm a chemist.)
37926
emilyrose gave a very thoughtful answer. \n\nReality on a small scale is quite a bit different than what we experience on our scale (the so-called "macroscopic scale"). I might make a few comments:\n\n1. Not only do the electrons in an atom have some wavelike properties, but the nucleus of an atom does as well. \n\n2. A "vacuum" is actually not really empty space, but a seething mass of virtual particles appearing and disappearing a very short time later (the Casimir effect is a strange force that is evidence for this mysterious force).
436453
I'm not sure I follow what you're trying to ask clearly enough, but maybe this will help.\n\nWhen A 'collapses' the wave function, he's affecting it, but not.  He gains the information about the entangled photons, but he hasn't actually changed the state of the photons.\n\nWhen B goes to 'look at' the entangled photons, he also sees the collapse.  However, wavefunctions only collapse because you see them as being in a defined state - it is impossible to look at something without it being collapsed.  B cannot observe photons in jar 1 to be non-collapsed.  By looking at it, it's collapsed.\n\nThere is debate whether these wavefunction collapses are due to our observations or simply a description of our lack of knowledge prior to observation.  Taking Schrodinger's cat... observing the cat does not change whether it is dead or alive, it merely collapses the 'wavefunction' of the cat's existance to being either alive or dead.
1165566
Your question, although it sounds absurd, probably has some research you could find on the topic. It is amazing how theoretical the major branches of science, which actively rely on theory assumed to be true in every day application, still are. I'd apply my brain to it but I gave up this particular line of thinking (which brings up the point to place here why I'm posting) after reading a Linus Pauling book section several years ago where he begins to introduce the "idea" of distal electrons taking up spaces on atoms and molecules locally, yet the bond slots they should be in are locally empty. The basic gist was, nobody knows if its true (mainly because they can't prove it) however, effects observed locally can't be explained without excepting the theory that an electron billions of light years away can be attached to a local, apparently empty electron bond slot.
305772
Seems to me that if you can manipulate 2 particles into entanglement (let's say one in New York, one in LA), then you can also manipulate a third particle (in Chicago) to the qualities measured in the first.  Sorry mathematician, but your two/three particle wave function theory although fascinating doesn't apply
1093639
What meant Indeed ?\n\nIt is not a easy question. This question was originally highlighted by Niels Bohr in the Copenhagen interpretation, where a system stops being a superposition of states and becomes either one or the other when an observation takes place. This makes apparent the fact that the nature of measurement, or observation, is not well defined. In other words we can measure position, but not the velocity or we can measure velocity, but not the position. \n\nI did mention Schrödinger's cat did not I? The Schrödinger's cat paradox suggests that by the act of quantum measurement we are destroying the object of measurement and hopefully not before we obtain one particular property. \nhttp://en.wikipedia.org/wiki/Schr%C3%B6dinger%27s_cat  \n\nSo by ‘measurement’ in QM we mean “In classical physics the mathematical model talks about the things we observe. In QM the mathematical model by itself never produces observations. We must interpret the wave function in order to relate it to experimental observations.” http://www.mtnmath.com/faq/meas-qm-2.html   \n\nI hope that tickles you, but I suspect you knew the answer.
407070
The short answer is that it simply isn't derived. \n\nStandard quantum mechanics is based on a series of postulates which describe something called a wavefunction. One of the postulates states that the wavefunction must obey the Schrodinger Equation.\n\nThe Schrodinger Equation is somewhat analogous to F=MA (Newton's Second Law) from classical mechanics. There really isn't any derivation of F=MA, it just seems to work. If you are doing an experiment with classical mechanics and you plug the right numbers into F=MA, you get the right answer. Likewise with the Schrodinger Equation, except it works on the quantum scale.\n\nThere have been some attempts to derive the Schrodinger Equation from a grand unified field theory, but for all but the most advanced particle physics applications the Schrodinger Equation is simply taken as a postulate. (just like F=MA)
416146
yes in the quantum world. hey and if no one reads this answer have i really typed it??
283261
A BEAM of particles behaves like a wave\nas you know. The wavelength is h/mv.  (De Broglie)\nInteresting is your question: do moving partikels create a wave? I cannot say yes or no. I will think about it very carefully. fd_r@yahoo.com\n\nAdded later. You suggest space/time is waving.\nTo me space and time are nothing physically. It is only fantasy in man’s brain and it works usefully.\nEinstein is talking about curved space. I cannot imagine that. I can only understand curved matter like a rubber ball and a standing wave in a string of a guitar. I cannot grab space and bend it.\nIn the same way I cannot visualise the concept of an oscillation of space, so an oscillation of nothing.\nMore acceptable for me is an electromagnetic wave as a cluster of oscillations of the electric and magnetic field.\nI do not reject your concept of waving space/time. I only cannot imagine. Maybe I am too simply minded. Maybe with waving space/time there is a field, not electromagnetic, because a beam of neutrons shows wave behaviour as well. What kind of field? Gravitational? I do not know.
1186592
In the quantum mechanical model of the hydrogen atom, the location of the electron is expressed in terms of a probability distribution, so one speaks of the probability that an electron will be found at a particular location near a nucleus. The probability distribution, in turn, is determined by a mathematical function known as a wavefunction, denoted y. Wavefunctions for the distribution of particles are a general feature of quantum mechanics, and for electrons in atoms they are known as atomic orbitals. The name orbital is intended to express a distribution that is less precise than the explicit orbits of the Bohr model. The probability of finding an electron at a specified location is proportional to the square of the amplitude of the wavefunction at that point. Hence, the sign (positive or negative) of the orbital is not relevant to the location of the electron, because taking the square of y eliminates any negative sign it may have.
801633
Hi, \n\nThat's too much like real work, but think about it like breaking pool balls in classical, and wave interference with quantum. \n\nHope that helps, \nMatt
1155114
We live in a universe of observable/measurable quantities. For example, length, width, height, time, mass, etc.  If different quantities cannot be expressed in terms of the other quantities, they are "orthogonal" to each other - you can think of them as being separate dimensions. For example, on an X-Y graph, the x-dimension is independent of the y-dimension because you cannot express a "y" quantity as a combination of "x" quantities. \n\nSpace has 3 dimensions (length, width, height); time is a fourth dimension that cannot be expressed in terms of the other three.\n\nAn n-dimensional space is just a space that is characterized by "n" orthogonal quantities - quantities that cannot be expressed in terms of each other. To completely define the space/universe, you only need to specify "n" values - any more than that would be superfluous because the other values would be some combination of the other orthogonal quantities.\n\nExample: if we lived in a 4-dimensional space characterized by length, width, height, and time, all you need to do is specify those 4 quantities to uniquely determine any point in that space.  If we add another quantity (such as temperature) that cannot be expressed in terms of the other 4, we now have a 5-dimensional space that requires 5 quantities to be specified.
693887
Imagine you have have a source that emits pairs of electrons. Quantum Mechanics now states that one can not describe the behaviour of each electron separately, but only the pair as a whole. \nFor instance, if the spin of the first electron is pointing up, than the other must point down and vice versa.\n\nBut QM also states that the exact state of an electron (up or down) can only be known if we measure it and not before. But once we measure the spin if the first electron (say, it's up) than we know immediately the spin of the second one too, although it might be lightyears away. And if some distant observer measures that spin he will find that it is down. So somehow, the information of the fact that we performed a measurement on the first electron, has travelled to the second electron. And at a speed, faster than light.\n\nThis is the EPR paradox.\n \nBut the story is not complete yet.\nSpin must be measured relative to an axis, be it x, y or z.\nBell's equations described how a measured along one axis on the first electron is related to measurements along the two other axis performed on the second electron.\n\nSee here for a more complete explanation:\n  http://en.wikipedia.org/wiki/EPR_paradox
340728
This is one of the best questions i have come across.In fact most Physicists have taken this cue for unravelling the problems of quantum mechanics. Look at the universe. Everything is moving in eleptical orbits. The sea shore is never straight and so are the trees, mountains and the rivers. The big bang and oscillating universe theory talks of tangential motion arrived through circular motion.\nStraightness is unnatiral!
1163983
Orbital does not mean where an electron is.  It means it is the highest probability of where the electron exist around the nucleus.  Heisenberg said it is impossible for us to know where the electron is (since it is always moving) thus we have calculated wave functions....regions of high probably of where the electron PROBABLY is.