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Do electrons really spin?

  1. Jul 6, 2010 #1
    So I was thinking about this right...

    We know from the double slit experiment that electrons have particle properties when they are "observed" (I prefer interacted with) and a wave function when left to their own devices.

    Now, lets take the Hydrogen atom for simplicity sake. It is classically stated that the electron spins around the nucleus. Well, that gives me a headache. The way I see it, the electron exists as a cloud of probability surrounding the nucleus. With respect to every plank "distance" or plank "space" in the "electron cloud" the electron both exists and doesnt exist at the same time. So, if the electron is everywhere and nowhere in the cloud at the same time..........how can it be spinning? (when I am saying everywhere and nowhere I am referring to what is now defined as "probability")

    Follow up question...

    for argument sake...lets say that the electron is more probably in one place, than another, per plank time. In the next instant of plank time....how do we know it is following a spin path of probability rather than statically popping up at random anywhere inside the "electron cloud"?
     
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  3. Jul 6, 2010 #2

    alxm

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    Welcome to PF.

    Okay, well that's not quite it. Depending on how you set up the double slit experiment, you may be 'observing' the electron acting 'particle-like' or 'wave-like'.

    Well you usually say it classical 'orbits' the nucleus. Spin is a distinct property from spatial motion. (mostly anyway) It does not correspond to rotation around its own axis, although that was the original idea (briefly held in the 1920's), hence the name.
    In any case, yes you have a "cloud" (electronic orbital) describing the probability distribution of the electron around the nucleus. But the electron still 'moves' in the sense that it has kinetic energy (among other things).

    Planck units have no special significance (apart from being a convenient unit) as far as anyone knows for certain. So I don't know what kind of significance you're ascribing to it here. But the electron exists at all times. It just doesn't have a definite location. But that's not exactly a prerequisite for existence.

    Electrons don't follow any 'spin paths of probability'*, or any trajectory in the classical sense. All you have is the probability distribution. Once you detect the electron at some point, the wave function 'collapses' (in the Copenhagen view) and you no longer have the same probability to find the electron at another point within the 'cloud. If you could measure it at, say, a Bohr radius away from the nucleus and then detect it a Bohr radius away on the opposite side after only one Planck unit of time, the electron would be moving much, much faster than the speed of light!

    (* Unless you're referring to the spin-dependent momentum field for the electron in the Bohm-de Broglie interpretation)
     
  4. Jul 6, 2010 #3
    OK. A little background is in order. Most of my understanding of physics comes from a high school course and a college course or two. I also have a doctorate in a non-scientific field. The rest of my understanding has been self taught. I have been reading articles and various other things I find on the internet. I think this is important because you seem well grounded in physics. However, that can be a double edged sword...because...what if some of the theories you cling to...are incomplete. So, in that spirit, consider me a fresh perspective on quantum physics.

    Alxm, thanks for your response. I wish to respond to your 4 quotes in 4 responses below. I will not repeat the above for brevity sake, but will number them 1-4.

    1. I think we are having trouble with the term "observing". When I say observing, I am referring to the measurements of (photons/electrons) passing through the 2 slits. Sure you could say that I am observing the (photons/electrons) hitting the back screen, but in this description I am only using "observation" as the measurements taken at the slits. Also from what I read, they used "screens" of some form or another at those slits to take the measurement. To me, that is "interaction"...meaning the (photon/electron) has to interact with some atomic structure (the screens at the 2 slits) before it moves on to the main screen that it "hits" to form the pattern. The way I understand it...and I like this description better....when the (photons/electrons) in their "probability wave form" are forced to interact with an atomic medium in both slits...the "measurement" they are...in effect..."put to the question"...they have to condense to a "particle form" and select one or the other slits...their "wave form" collapses into "particle form". When there is no "observation" or "measurement" or "interaction"(all three same meaning)...the "wave form" encounters the 2 slits and passes through "both" and "neither" at the same time...the "wave form" also interacts with itself heading toward the "hit screen" thus creating a wave like pattern. The "wave form" is also very important for my next 3 answers because in my understanding...when that "wave form" passes through both slits, it occupies a space conically equal to every probability location in space that it could occupy before it hits the hit screen. In a way, its like a giant funnel cloud of probability pointed at the "hit screen".

    2. does it "move"? does it have "kinetic energy"?...in the classic sense...I'm not so sure. I will elaborate more on this in the next two questions.

    3. I like using plank space and plank time because helps to illustrate my point. In physics today I think that "black hole" theorists and "string/m" theorists are the only ones messing with plank space. Plank space is the furthest distance a photon can cover at the speed of light per plank time. I like to think of it as bubbles of space time...a matrix if you will...a unit of space time...I have more theories on that..but Im trying to keep this simple.....lets say that there are a quadrillion "units of space time" surrounding the nucleus....lets say...that per "wave form" function of an electron....the "wave form" is occupying a probability state in every one of those quadrillion "units of space time" at the same time....if so...they aren't really moving are they?...they only give the appearance of movement when "observed" or "measured" or "interacted with". They appear to have "kinetic energy" when "observed" or "measured" or "interacted with".

    4. I like the use of "Bohr radius" it states that the electron is "more probably" in one location of the cloud than another. Lets go back to my "plank space" or "unit of space time". Bohr would say...that in one instance of "plank time" the electron is more probably in this point in "Bohr's radius"....so....in the next instant of "plank time" it is more probably somewhere else in the Bohr radius. Now lets go back to "electron moves" and "kinetic energy". Lets use the earth as points on Bohr's radius and the "electron cloud". Lets use people as examples of the electron. And, lets use 1 meter as the "unit of space time". Now, the way I see it...for every meter on earth there is a person. But, not really a full person but a ghost of a person...both there and not there at the same time. Lets say the equator is the Bohr's radius. There are ghosts all around the equator but they are more substantial...or...more "probably there". So, when asked where the "electron/person" is on earth...it is everywhere but more probably on the equator. Now, lets use plank time....and lets use one person on the equator as the most probable location of the "electron"....the most substantial ghost. Well...from one unit of space time to the next...the "most substantial ghost" moves. Now, if we hold to "kinetic energy" and "electron moves" and "spin"....that "substantial ghost" will move a meter away from his last location...in any direction...most likely along the equator. However, in my view...that "most substantial ghost" will blink out of existance in space time 1 along the equator and pop up in bolivia....in the next instant....will pop up in antarctica....in the next instant pop up in Moscow...in the next instant pop up along the equator...because he mostly pops up around the equator. My point being...that in an electron cloud "electron movement" "electron spin" and "kinetic energy" can not be used to describe the electron. The electrons highest probability of location is not "moving"..but "blinking in and out of space time" all over the electron cloud per unit of plank time. It is random.

    4b. you say "If you could measure it at, say, a Bohr radius away from the nucleus and then detect it a Bohr radius away on the opposite side after only one Planck unit of time, the electron would be moving much, much faster than the speed of light!"...right...but it isnt really "moving" in the classic sense. This is going to be hairy to describe...and it would involve another theory of mine on what space time is...kinda another string theory...but anyways...ill use a short cut here instead of this theory I am working on. Think of the "probability wave" or "most probable location of the electron" as following the rules of "entanglement" or "spooky interaction". We know "entanglement" doesnt break the classic speed of light laws..yet..they can transmit non-classical information instantly from atom to atom. I submit that the "probability wave" of the "electron cloud" operates in the same way.

    I would love to hear your rebuttal. I find your insights most helpful. Same goes for anyone else who would like to chime in.
     
  5. Jul 6, 2010 #4
    I found something new I would like to tackle alxm...this statement...

    3b. you say "But the electron exists at all times. It just doesn't have a definite location."...That sounds like the EPR paradox to me. And, wasnt that cracked by Bell's Inequality?
     
  6. Jul 7, 2010 #5

    alxm

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    Well my doctorate is in chemical physics and my specialization quantum chemistry. So basically I've spent about 10 years, full-time, thinking about the quantum mechanics of electrons moving around atoms.

    They both would constitute observations. My point was that there is more than one double-slit experiment. If you measure the slits to determine which one the particle passed through, then you see 'particle-like' behavior and no interference pattern. You don't necessarily have to measure the slits to see this, though. You could for instance measure their time-of-flight to determine which slit from the difference in distance. The point is whether or not you can (in principle) determine which slit the particle passed through. How the measurement is done doesn't really matter.

    Electrons in atomic systems move. They do not move classically, by which we mean that they have a definite location and/or momentum, or follow a trajectory such that their location/momentum at some later point in time can be exactly determined if these values were known at an earlier point in time. They do not move in the sense that their wave function is (in the ground state) stationary; the probability distribution does not change with time.

    They do move in the sense that they do have kinetic energy. They "move" in the sense that quantum mechanical motion becomes classical motion at the classical limit, and so there's no meaningful distinction between the two - it's a sliding scale. They "move" in the sense that their kinetic energy is affected by the non-linear dynamics of many-body motion. It's routinely described as 'motion', even though it's understood that the classical equations of motion do not apply.

    For the second time: Space is not quantized in units of the Planck length. Planck units (the name is Planck btw, nothing to do with planks) is just a system of units which are convenient when dealing with certain equations, because it eliminates certain constants, making the equations dimensionless. Depending on the equations, they may or may not be a convenient choice (e.g. for describing electrons around atoms, http://en.wikipedia.org/wiki/Atomic_units" [Broken] are more convenient). Converting to dimensionless form is a general approach when solving any equations, especially differential equations. It doesn't imply anything physically.

    Now there is some speculation about possible physical significances of Planck-unit quantities. But that's not going to help you understand basic QM any better. In this case it's simply wrong - the wave function is not quantized in units of Planck distances. Rather, it's a fundamental postulate of quantum mechanics that it http://hyperphysics.phy-astr.gsu.edu/Hbase/quantum/qm.html#c4" in x.

    A standing wave doesn't 'move' in one sense, but it does move in another, the quantum mechanical situation is analogous.

    It's natural that the electron is 'more probably' in one location compared to another. This is a general and fairly trivial consequence of the fact that the wave function is normalized. The total probability of finding the particle anywhere in the universe must be exactly 1, so the probability distribution/wave function cannot be constant* over all space. Physically it's also fairly straightforward: Naturally a negatively charged electron will more likely be in the vicinity of the positively-charged nucleus.

    That's not what Bohr would say. (To begin with, he never attributed anything special to Planck units either) Bohr would say that when you measured the particle in a particular location, the wave function (probability distribution) 'collapsed', and the particle was now exactly in that location. The probability of the particle being in any other location then was exactly zero. Following that observation, the probability distribution returns to its old state via the time-evolution of the wave function. It takes an amount of time before it returns to its previous, indeterminate, state. This is much longer than the Planck time.

    On the contrary - the probability 'cloud' is directly related to the energy (including kinetic energy) of the electron. That relation is the Schrödinger equation.

    What I meant by this was not that it was "not moving in the classical sense" (what I meant by that is elaborated upon above). What I meant was that this simply does not happen. Quantum mechanics does not allow particles to move at superluminal velocities. The wave function propagates at a finite speed.

    It doesn't. It's worth noting that when one talks about an 'electron cloud' or 'probability density' or 'charge density cloud' of an atomic electron, you're talking about the absolute square of the wave function, i.e. the solutions to the Schrödinger equation. These are derived results from quantum mechanics. Using a result of quantum mechanics to state something which is at odds with quantum mechanics is at best logically inconsistent.

    The EPR paradox regarded whether the particle had a definite location which was merely unknown (a 'hidden variable') or whether it had a truly undefined location (or any other property). The existence doesn't enter into it. The results of Bell's theorem and Bell-test experiments indicate that either the latter is true or at the very least, that the nature of which kinds of 'hidden variables' that can exist is seriously curtailed.


    Finally, I'd just like to say it's easy to come up with a "big idea" on how something works, especially if you don't know a lot about the subject and especially if you're working on your own. Because the idea you get is simply wrong, yet you don't know enough to know why it's wrong and there's nobody there to tell you it's wrong. If the person has a certain personality type, they may get so enamored with their idea that they refuse to be convinced once someone does show them what's wrong with their ideas - and thus another "crackpot" is born.

    So, do you want to approach this like a scientist - with humility and in full expectation that you might be wrong, with interest in finding out what's wrong with the ideas, so that you may learn something. Or do you want to approach this like a crackpot and insist your ideas are right and that you have nothing to learn?

    I hope you don't get offended, as I'm not accusing you of being a crackpot (yet). But this forum gets so many of them that it has pretty strict rules on 'personal theories'. So any post along the lines of "I don't have a degree in physics but I have a new theory about how [advanced concept] works" raises some big warning flags.

    (*With the exception of a universe that's a 1-dimensional loop and some other unrealistic geometries)
     
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  7. Jul 8, 2010 #6
    OK...

    For the "measurement"...any "measurement" that collapses the wave function....is there "interaction" with a measurement medium. Like....the wave and a atomic particle measurement medium...or the wave and a photon or electron hitting it medium. Caught in a magnetic field medium. I guess what I am asking...for any "observation" or "measurement" however taken....is there an interaction with a physical medium?...I think that is all that is important.

    You say..."They do not move in the sense that their wave function is (in the ground state) stationary"...I hear "they dont move"....which I think was my point to begin with.

    You say..."the probability distribution does not change with time." Now, that is interesting, and also why I like to bounce these ideas off a physicist. So, in my "earth as the atom" analogy....per time...the "most substantial ghost" does not move. In other words...there are ghosts at every meter of the earth...some more substantially at Bohr's radius...but per time...does not move....kinda a frozen medium of more substantial and less substantial ghosts.

    you say..."They do move in the sense that they do have kinetic energy. They "move" in the sense that quantum mechanical motion becomes classical motion at the classical limit, and so there's no meaningful distinction between the two - it's a sliding scale. They "move" in the sense that their kinetic energy is affected by the non-linear dynamics of many-body motion. It's routinely described as 'motion', even though it's understood that the classical equations of motion do not apply."....so...what I hear is when there is interaction with the electron and the wave form collapses it can be described in terms of kinetic energy as it interacts? (I may be a little wobbly on that...I dont know what "non-liner dynamics of many-body motion" is)

    You say..."Space is not quantized in units of the Planck length"...right right I concede that point. I was just using it to illustrate a point. But isnt this the area of speculation for physicists? String theory, M theory, quantum foam, black hole singularities...I could probably work expansion in there too. Point being, plank space is not really understood by anyone. I was just dipping my toes in it to make a good analogy. Im not trying to overturn Quantum Mechanics or anything.

    you say..."On the contrary - the probability 'cloud' is directly related to the energy (including kinetic energy) of the electron. That relation is the Schrödinger equation"...I think I see...I have abandoned the idea of a "most probable ghost" that moves. Thanks for your help on that...and what I think I am reading here is that via the Schrodinger equation as the wave form collapses into particle....the electron can be described by kinetic energy on a sliding scale as it approaches and becomes the particle. In other words..as the electron becomes more particle like it becomes more kinetic energy like? Is that it?.....If that is it...what I am saying is that when the electron is in wave form....it does not move. It does not have kinetic energy...however potential kinetic energy...because it could always collapse into a particle through interaction? Is that it? or am I way off?

    you say..."What I meant by this was not that it was "not moving in the classical sense" (what I meant by that is elaborated upon above). What I meant was that this simply does not happen. Quantum mechanics does not allow particles to move at superluminal velocities. The wave function propagates at a finite speed."....this point is moot now because in wave form...from time A to time B...nothing moves...it is all more and less substantial "frozen ghosts". However, I did have a thought...I understand that particles cannot move at superluminal velocities.....but can probabilities in the probability wave move faster than light?...for instance...in the double slit experiment...one electron at a time...where the electron interferes with itself through probabilities.....can that "communication" between probabilities move faster than light?.....just a thought I had.

    you say..."Using a result of quantum mechanics to state something which is at odds with quantum mechanics is at best logically inconsistent." Im not sure exactly what I did that was inconsistent...could you explain?

    Oh yah, I could be completely wrong. I didnt mean to ruffle your feathers. I find this discussion very educational. I already modified some of my ideas. Thank you for your input. Oh, also, is there a place where we could discuss "big ideas"? because I have a few...and if this isnt the proper forum to bounce some of my ideas off of physicists...could you direct me to such a forum?
     
  8. Jul 9, 2010 #7

    alxm

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    Yes, the definition of 'measurement' in quantum mechanics is pretty critical. The most general description I can give is that measurement constitutes an interaction with the macroscopic environment, with things-at-large. In other words, the 'measuring' thing is acting classically, not quantum-mechanically. The wave function does not 'collapse' when two quantum mechanical particles interact and the whole system is acting quantum-mechanically. It's a long-standing question how one gets from one state-of-affairs to the other, which was illustrated by the famous 'Schrödingers cat' idea. We've learned a bit about the process since (called 'decoherence'), but it's not fully understood.

    It has to be described including kinetic energy, before it "collapses", it's part of the Schrödinger equation, which defines the wave function. If electrons did not have kinetic energy, there would just be the energy from the attraction of the nucleus, and they'd have no reason to not 'fall in'. The reason why they do not, is because the have kinetic energy, which increases if they occupy a smaller space. (In introductory texts this is often rationalized using the Uncertainty Principle; if they occupy a smaller position, they have lower uncertainty in position, which must mean greater momentum)

    What I mean by non-linear dynamics here is simply that if you have a system of three moving bodies, e.g. the Earth, Moon and Sun, each exerting a force on the others, then the motion is complicated; the position and motion of each one depends on each other one. This leads to a nonlinear differential equation, which cannot (in general) be solved analytically. This is the case both with classical and quantum mechanics. It's called the many-body problem.

    So if you were to regard an electron as a simple density 'cloud', then the potential energy between two electrons (and the electrons and nucleus) would simply be the repulsion/attraction of these densities.

    But what about the kinetic energy? Well, you could treat that as if the electrons were simply moving in the density it 'sees' from each other atom, in other words, each electron could be treated as moving in an averaged field of every other electron. We do this; it's called the Hartree-Fock approximation. Why approximation? Because it's not accurate - they don't move as if they were moving in a mean field, they 'avoid' each other when moving to a certain extent - and this change in their wave function/pattern of motion lead to a change in kinetic energy, termed 'correlation energy'.

    So despite the fact that the wave function does not change with time and is 'stationary' for a many-electron atom, there's an real and measurable change in energy that's due to their motion. (Or at least conceptually very difficult to rationalize without invoking motion.) If anyone doesn't think this is weird, they haven't thought about it enough. :smile:

    Well there is some. And I'm hardly up-to-speed on every speculative theory out there either. But it's a point I had to make because there seems to be a lot of accounts out there telling people quantum mechanics holds that the universe is made of 'pixels' (for lack of a better word). It does pop up here a lot. Anyway, any theory which explains quantum mechanics in such terms will still have to explain why space is apparently continuous at QM scales, so if you're talking basic QM, then space is continuous, and the fact that this might not hold at another scale is a different matter. (Much how velocities are additive as far as classical mechanics is concerned, even if we now know this is only true at non-relativistic speeds)

    Well, no. Both particles and waves can have kinetic energy. But when the momentum (which is classically mass x velocity) increases, things act more "particle-like" in the sense that they have a more definite location. Classical objects have large mass, and therefore higher momentum, and therefore have a more well-defined position.

    This is subject to interpretation. But in some sense it's correct, yes.

    There's nothing wrong with asking questions, or thinking about stuff. Just follow the https://www.physicsforums.com/showthread.php?t=414380" and you'll be fine. The defining characteristic of the 'crank' is whether or not they accept that they're wrong or not. But this is the internet, so there are of course places for them too. There are whole web-communities of perpetuum mobile builders out there.
     
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  9. Jul 9, 2010 #8
    alxm, whilst you're answering noob questions, I'm wondering:
    - I spoke to a deBB'r and he told me that in decoherence the wave function is simply "bunching up" to a pointer like state during thermal interaction. Is this a correct picture? And does this "bunching up" still entail some sort of superposition even after reduction?

    Haha.
     
  10. Jul 9, 2010 #9
    Awesome answers ALXM...got a few follow ups...

    regarding decoherence...so...in the double slit experiment...when the (electron/photon) is fired at the slits...when the (electron/photon) is passing through all the atoms that make up the air....there is no decoherence because the transparent nature of the atoms are acting quantum-mechanically. That, only the measuring medium is acting classically and causing decoherence?

    OK...I am still having difficulty wrapping my noodle around the electron having "kinetic energy" while it is in wave form. Classic Kinetic energy is the energy it possesses due to motion. Lets start there for simplicity sake.

    You say..."It has to be described including kinetic energy, before it "collapses", it's part of the Schrödinger equation, which defines the wave function."...I say...yes it works in the Schrodinger equation because if you really dont know what is going on behind the curtain, it is fine to gloss over it and call it kinetic energy....the equation still works (now dont flip..im not trying to overturn Schrodinger...you gota read the whole thing).

    You say...If electrons did not have kinetic energy, there would just be the energy from the attraction of the nucleus, and they'd have no reason to not 'fall in'....I say...that is a simple "but for" argument. I agree that there is "something" keeping the "wave form" from falling in...but I have a problem calling that "something" kinetic energy.

    You say...The reason why they do not, is because the have kinetic energy, which increases if they occupy a smaller space....I say...that "something" increases if they occupy a smaller space.

    You say...(In introductory texts this is often rationalized using the Uncertainty Principle; if they occupy a smaller position, they have lower uncertainty in position, which must mean greater momentum)....I say...(In introductory texts this is often rationalized using the Uncertainty Principle; if they occupy a smaller position, they have lower uncertainty in position, which must mean greater "something")

    Now, im not trying to be annoying here, I just still have a problem with calling the something "kinetic energy". You could call "kinetic energy" in the Schrodinger equation "spaghetti monster" and the equation will still work. Might not translate as neatly when you come back to classical form because the "spaghetti monster" becomes "kinetic energy". But when you have an "electron cloud" around an atom, and that electron is occupying all space around that electron in lesser and greater probability fields. And, the lesser and greater probability fields do not move per time, I have real difficulty defining that as "kinetic energy". In a math problem it still works as "kinetic energy" for all "practical purposes" but I think that an electron in that state needs new language...maybe "spaghetti energy"...that is where my head is right now. I welcome rebuttal.

    Now you start to go into interacting electrons...this gets a little hairy for me....

    you say...So if you were to regard an electron as a simple density 'cloud', then the potential energy between two electrons (and the electrons and nucleus) would simply be the repulsion/attraction of these densities....I say ok ok...Pauli exclusion principle plays in here too I think.


    you say...But what about the kinetic energy? Well, you could treat that as if the electrons were simply moving in the density it 'sees' from each other atom, in other words, each electron could be treated as moving in an averaged field of every other electron....I say...you could "treat" it like that....but wouldnt it work better by saying that 2 interacting electrons occupy probability space relative to one another while never occupying each others space. This relative space occupation of 2 probability fields changes the shape and function of the overall field (both electrons)?

    you say...We do this; it's called the Hartree-Fock approximation. Why approximation? Because it's not accurate - they don't move as if they were moving in a mean field,[but can you say they even move when in wave form?] they 'avoid' each other when moving to a certain extent [I agree they avoid eachother] - and this change in their wave function/pattern of motion lead to a change in kinetic energy, termed 'correlation energy'[or...there is a change to the shape and function of the overall field...that function is tested when it acts classically]....at least that is the way I see it. I might be completely butchering QM but that is where my head is right now. If I am completely off, please let me know.

    you say...So despite the fact that the wave function does not change with time and is 'stationary'[yes yes] for a many-electron atom, there's an real and measurable change in energy that's due to their motion. (Or at least conceptually very difficult to rationalize without invoking motion.) If anyone doesn't think this is weird, they haven't thought about it enough....I say...for a many-electron atom, there's a real and measurable change in energy...(when measured classically)....that's due to shape changed double probability fields. As their "spaghetti energy" becomes "kinetic energy" for their real and measurable "classic measurements".........did you fall out of your chair yet haha.....again, I am completely open to any explanation as to why this is wrong. I value your input and am prepared to abandon concepts that are shown wrong.
     
  11. Jul 11, 2010 #10

    alxm

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    I'm not sure what he meant (or the deBB perspective, really).
    But thermal interactions has something to do with decoherence for certain. The basic idea is that when you have a macroscopic interaction going on, it lead to the creation of entropy, and the second law of thermodynamics kicks in and the system gets irreversibly 'locked in' to a state where it's either in one state or another, and the off-diagonal elements (coherences) in the matrix of states, where the system is "in both states at once", become zero.

    An example is an electron (a quantum mechanical thing) hitting a scintillation tube (Geiger counter), which releases a cascade of electrons giving a macroscopic 'detection'. The initial interaction, being all quantum-mechanical, is reversible. But the electron cascade is a big, entropy-creating event, which is not.
     
  12. Jul 11, 2010 #11

    alxm

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    Well typically you'd do the double-slit experiment in a vacuum. I'm not actually sure offhand whether or not interaction with air would be a large enough effect to destroy the interference pattern. I'd guess 'no' for a photon double-slit experiment but 'yes' for one done with electrons.

    Okay. Well you could, if you like, take the deBB view and say that it's the 'quantum force' which is balancing the nuclear attraction, and that the electron is in fact, completely stationary. But the mainstream view is as I said; that the kinetic energy term of the Schrödinger equation does represent kinetic energy.

    You say...The reason why they do not, is because the have kinetic energy, which increases if they occupy a smaller space....I say...that "something" increases if they occupy a smaller space.

    Well, this is where the 'wave' picture is more intuitive. Consider a http://en.wikipedia.org/wiki/File:Standing_wave.gif" [Broken] - it doesn't move in space, but it still has energy.

    The main reason we interpret it this way is because 1) the quantum mechanical kinetic energy then becomes the classical-mechanical kinetic energy as you go towards the classical limit and 2) the quantum-mechanical Hamiltonian which describes the system then looks like the classical one, where the kinetic energy is the momentum squared divided by 2x the mass. (only that in the QM picture the momentum is an operators rather than a variable)

    Well, not in the Hartree-Fock picture, because it's exact with respect to that.

    Well they can occupy the same space, just not have the exact same orbital (single-electron density) and the same spin. That said, we do this in the Hartree-Fock approximation, and essentially every other method used to calculating such things (most of which use HF as a starting point) The mathematical device to create such a description is called a Slater determinant. If you describe your system this way, it's impossible for two electrons with the same spin to be in the same state.

    I don't really know what you mean. Yes, the overall field of electrons is going to change if a single one changes.

    Well you can invent as many unobservable concepts you want.. but to what end? Occam's razor and all that.
     
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  13. Jul 11, 2010 #12
    Really good stuff alxm. I think I understand this all a little better now. Thank you for being so patient with me.
     
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