Talk:Quantum mechanics/Archive 4

Entanglement, 1905

Looking back on a certain historic event, it is possible to characterize the following as an type of quantum entanglement -- just view the clocks referred to below as Cesium clocks : Einstein's 1905 special relativity challenged the notion of an absolute definition for times, and could only formulate a definition of synchronization for clocks that mark a linear flow of time^[1]:

If at the point A of space there is a clock ... If there is at the point B of space there is another clock in all respects resembling the one at A ... it is not possible without further assumption to compare, in respect of time, an event at A with an event at B. ... We assume that ...

1. If the clock at B synchronizes with the clock at A, the clock at A synchronizes with the clock at B.

2. If the clock at A synchronizes with the clock at B, and also with the clock at C, the clocks at B and C also synchronize with each other.

• ^ Einstein 1905, Zur Elektrodynamik bewegter Körper [On the electrodynamics of moving bodies] reprinted 1922 in Das Relativitätsprinzip, B.G. Teubner, Leipzig. The Principles of Relativity: A Collection of Original Papers on the Special Theory of Relativity, by H.A. Lorentz, A. Einstein, H. Minkowski, and W. H. Weyl, is part of Fortschritte der mathematischen Wissenschaften in Monographien, Heft 2. The English translation is by W. Perrett and G.B. Jeffrey, reprinted on page 1169 of On the Shoulders of Giants:The Great Works of Physics and Astronomy (works by Copernicus, Kepler, Galileo, Newton, and Einstein). Stephen Hawking, ed. 2002 ISBN 0-7624-1348-4

Quantum Physicists are just catching up with Relativity!

I understand quantum mechanics just enough, not to make any great discoveries in the field, but enough to understand the basics. Special Relativity is the same way. I found something interesting though, relativity implies both wave-particle duality and supersymmetry! A wave is a carrier of eneergy from place to place. A paritcle can be viewed as a carrier of mass from place to place. Relativity says energy is the fourth-dimensional extendsion of momentum (which is mass times velosity). This implies that waves are fourth-dimensional extendsion of particles! This also implies that the carriers of energy (Bosons) are extendsions of the carriers of mass (Fermions)! Wave-particle duality and supersymmetry. It seems so simple I'm surprized that this was overlooked for so many years.--SurrealWarrior 18:35, 20 Jun 2005 (UTC)

Reverted contribution.

If we are going to retain the "Bohm interpretation" which is "not popular among physicists", surely we also need the main stream interpretation that I was taught in graduate school by famous physicists. I propose including the following:

"According to a lecture by Herbert P. Broida to his students at UCSB, the probabilities and other difficulties always come from the relation between quantum and classical physics, not from quantum mechanics in isolation. To explain the meaning of this, since Classical Mechanics is now only an approximation to quantum mechanics (the same approximation as Geometric Optics) and not an independent theory, this makes the probabilities belong to classical physics, not to quantum mechanics. The difficulty is that one cannot do any experiment without using Classical Mechanics to describe the apparatus."

There is also a problem that the "interpretations" listed here don't confine themselves to philosophical interpretation. The "Bohm interpretation", as described, is physically verifiable and therefore physics rather than philosophy. The "Everett many-worlds interpretation" on the other hand is so unverifiable that it is not even philosophy.

Quantum mechanics has become established, over a full century and is in no way in question. If it were in question, that would be a matter of physics, not philosophy. The philosophical issue is how to speak about it. The way that research physicists do speak about it is to call the quantum wave function "reality" and Classical Mechanics an "approximation".

David R. Ingham 4 July 2005 17:48 (UTC)

I think the paragraph is vague, except for the last sentence: "The difficulty is that one cannot do any experiment without using Classical Mechanics to describe the apparatus." With a little more clarity, this is more of a measurement in quantum mechanics type of contribution. Also, skip the Broida reference unless you want to explain who he is. PAR 4 July 2005 19:59 (UTC)

I'll think about it some more. I strongly feel that it is wrong, to ascribe probability to quantum mechanics, when it really belongs to the Classical Mechanics (= Geometric Optics) ray approximation to the quantum mechanics of massive particles, and to the zero energy per particle approximation to the quantum mechanics of light and sound. The Copenhagen Interpretation did not go far enough in this direction. The statement that "all of the mathematical consequences of quantum mechanics can be trusted" is enough to get right answers, but it is not philosophically tidy— One might be led away from using wave packets to account for details of the interaction between microscopic and macroscopic systems, when they are needed. David R. Ingham 5 July 2005 23:23 (UTC)

I sympathize. I have my own personal points of view on quantum mechanics, which are at odds with or not addressed in this article, but I don't think this article is the place to air them. This article should contain only those aspects of quantum mechanics where there is rather broad agreement, and a list of contentious areas with enough information so that someone who is interested can follow up. PAR 5 July 2005 23:45 (UTC)

I agree. Karol July 6, 2005 07:31 (UTC)

The Ultimate Unified Theory?

It seems that in the 20th century, Quantum Mechanics and Relativity are the only leading theories, because General Relativity is not capable of describing the beginning of the universe etc., another "ingredient" is required to make the "recipe" perfect, and it seems that Quantum Mechanics is the best candidate. If unified, the new theory shall be named as Quantum Theory of Gravity, which Wikipedia has an excellent on it, we should start working! For information on the grand unified theory, superstring theory is the best candidate that can unify everything, I am not very sure about that, and superstring theory also seems to be the most popular theory. When you try to apply to work as a researcher in a physics working office, it seems that you will be instantly selected to work in their office if you study superstring theory, and if you study other theory, they will consider considering you as their researcher colleage, which is quite a pain. Anyway, I think that a unified theory, or the Grand Unified Theory (which is quite of an exaggeration) is definately needed to describe our own cosmic habitat. Feel free to email me to discuss about issues on quantum mechanics and physics etc.: timothyphtse@gmail.com

uncertainty principle

i have a question about degenerated matter. when a star shrinks, the maxium uncertainty in the position of a particle for example electron decreases, so it minimum uncertainty in momentum increase. what i dont understand is what is uncertainty in momentum? does it mean that the particle is traveling with multiple momentum at the same time? because i read from somewhere as the minimum uncertain momentum increase the particle's minimum velocity increase, and i just dont get it (is it like the particle's velocity can be 0-something?)

Yes, a particle does have multiple momenta and multiple velocities at the same time, just like a particle of light goes through both holes in a diffraction experiment or through both sides of the lens of a camera or telescope. To really understand this you have to accept that the description of a particle's motion with a single momentum and single position is an approximation that breaks down on a very small scale. It is the same approximation as Geometric Optics. To really understand quantum mechanics you need to give up thinking that a particle really is in a single place. The only reality (though not the only mathematical description of reality†) is the wave function. If you want to get closer to what you see directly, take up art or literature. --David R. Ingham 17:59, 18 July 2005 (UTC)

†The Heisenberg formulation does not take the form of a function.

• Robert Martin Eisberg, Fundamentals of Modern Physics, John Wiley and Sons, 1961, p. 177

--David R. Ingham 04:41, 26 August 2005 (UTC)

Bohm interpretation

There seem to be other problems with this paragraph, besides not being elegant physics. The Schrödinger equation is not a function but a unique and explicit formula for the time development of the wave equation. Non-locality is a property of equations, not of functions. If distant particles interact instantaneously, that is not described by the Schrödinger equation, which is local. Non-locality is physics and not philosophy. --David R. Ingham 21:19, 24 July 2005 (UTC)

Improvement Drive

A related topic, Astrophysics is currently nominated on Wikipedia:This week's improvement drive. Come and support the nomination or comment on it.--Fenice 07:31, 6 August 2005 (UTC)

spin

can someone please tell me what is spin? i heard it can be oriented in up and down and its parallel/antiparallel to the local magnetic field, but whats all that "spin 1/2, 2,1, 0"? like everywhere i read about spin it never says what it is, only it is an intrinsic angular momentum. what does that mean? maybe i just dont know when it is telling what it is, can someone just tell me in ordinary language? (not like everyday language, just dont use a technical term in every sentence)

thanks

-protecter

To begin with, it is the angular momentum of a particle, in units of ℏ (h bar is Planck's constant deviede by 2 π). Angular momentum can change only by integer multiples of ℏ, that is, it is quantized. --David R. Ingham 23:45, 8 August 2005 (UTC) Revised in format--David R. Ingham 16:34, 9 August 2005 (UTC)

---

angular momentum tells you stuff like how much how long you'll have to apply a torque to something to get it to stop moving, and how fast other things will will start spinning if they collide with that something. Angular momentum usually comes from things that are rotating, but elementary particles also have a built-in angular momentum, just like they have a built in charge. The total angular momentum of something is the sum of all the intrinsic angular momenta as well as the orbital angular momenta (which are the angular momenta that come from rotating).

you can't take away intrinsic angular momentum from a particle, it's always there, so the analogy with torques and collisions doesn't apply. But you can still tell that the intrinsic angular momentum is there from things like the dipole moment (electric or magnetic) of a particle.

The number you hear associated to spin (0, 1/2, 1, 2) tells you how the thing behaves under rotation. Like, a dipole behaves like a pointing finger, when you rotate it 30 degrees, the finger points 30 degrees further. Other things behave slightly differently. Like if you rotate your coordinate system 30 degrees, and consider the moment of inertia of an object, you have to apply two 30 degree rotations to two coordinate axes to get the new moment of inertia. That's because moment of inertia is a second rank tensor.

So that spin number really tells you how things behave under rotation. Electric fields behave like vectors, and anything that behaves like a vector is called spin 1. anything that behaves like a second rank tensor is called spin 2. things that behave like invariants (look the same no matter how you rotate) are called spin 0.

And when you add quantum mechanics into the mix, you gain the possibility of things that have half integer spin. These guys pick up a minus sign when you rotate all the way around.

according to the spin statistics theorem, spin also determines whether things act like fermions (with the Pauli exclusion principle) or like bosons (which have no Pauli exclusion principle.

After you plug through some math, you find that the spin number, which tells you how things behave under rotation, is proportional to the angular momentum, which tells you how torques apply and how collisions happen. so spin tells you both how things behave when you rotate your coordinates, as well as how much angular momentum something has. the fact that some angular momentum is intrinsic just means that it doesn't come from rotating objects, but is just there. -Lethe | Talk 01:37, August 9, 2005 (UTC)

thankyou for your explanation, i have now a faint idea of what it means. however i am finding it a bit advanced for me. (never heard of second rank tensor). so are you basically saying spin describes the direction of the field (like dipole) around a particle under rotations? also, this may sound silly, when do they teach the full concept of spin?

-protecter

the easiest way to think of a second rank tensor is just to think of it as a 3x3 matrix (although that misses a lot of the meaning). when you do a change of basis to a matrix A, you have to multiply it something like D^TAD, where D is the change of basis matrix. The point is to notice that you have to multiply by the change of basis matrix twice, once on the left (which a transpose or inverse) and once on the right. A third rank tensor would get multiplied three times. This is one way to understand tensors, though eventually you'll want a more intrinsic understanding.

a vector is a first rank tensor, because when you change basis, the vector v goes to Dv. a vector can be represented by 3 components while a second rank tensor uses 9 components. So it's not 100% accurate to think of a second rank tensor as a pointing arrow. On the other hand, it is sometimes possible. (technical stuff: if the tensor is symmetric and traceless, for example. then it lives in a faithful irrep of the rotation group, and we can assign a unique rotation to it.)

so yes, to answer your question, the spin describes the direction of thhe field (like a dipole). that's the general idea. to understand it better of course, you'll have to learn the math.

so, where do they teach spin? of course, everyone's first introduction is in their Quantum Mechanics class, but I find that the lessons learned there are unsatisfactory. You'll get some more mathematical machinery in quantum field theory, although some of the more experimental particle physics text (Peskin and Schroder?) still leave you confused. The best way to learn it is to take a course in representation theory (of Lie groups, especially), and then just sit and think about how physical systems have to live in irreps of the rotation group (or its central extension, in the case of a quantum system). you will have learned what the irreps of the rotation group are in your representation theory course. there are 1, 2, 3, 4... etc dimensional representations. then you write down a field theory and discover that a system that lives in the n-dimensional rep has intrinsic angular momentum (n-1)/2. When you learn how to construct these representations, you'll see that the 1 dimensional rep is just a scalar (scalars have 1 component), the 2 dimensional rep is a spinor (spinors have 2 components), like you learn in QM, the 3 dimensional rep is a vector (3 components), the 4 dimensional rep is a spin-3/2 space like a vector times a spinor, the 5 dimensional irrep is a rank-2 symmetric traceless tensor, so that's what describes a spin-2 system. (2 = (5-1)/2)

To sum up, representation theory tells you what possible multicomponent guys there are that behave simply under rotations. how they behave under rotations tells you what their angular momentum is, and the rep tells you what kinds of objects can have that angular momentum. Quantum field theory books have the most relevant coverage, but they're notoriously hard to read if you don't already know what they're talking about. -Lethe | Talk 08:05, August 16, 2005 (UTC)

To sum up,

Spin of light

In quantum mechanics, the polarization of light and other wave length ranges of electromagnetic radiation is called the spin or helicity of the photons (particles). Linearly polarized light consists of photons that have a linear combination of positive and negative helicity.--David R. Ingham 17:33, 9 August 2005 (UTC)

quantum mechanics and general relativity, in the introduction

I am not sure about the statement that this combination is a problem, but I don't know enough to change it, at this time. The theory of the decay of black holes seems to indicate that the two can work together. As I remember, propagating gravitons (gravity particles) present no problem.

There is a very real problem in describing gravity quantum mechanically; Google for it. The Hawking black hole radiation theory is not really relevant, because it's only a "semiclassical" theory. You could say that it describes the effect of gravity on quantum mechanics, while ignoring the effects of quantum mechanics on gravity. -- CYD

What does this sentence in the introduction mean: "Often, it is the answer to questions when general relativity fails." ?
I find it a weak sentence and am going to change it but before I do that would someone like to pipe up if there is a deep signifigance to it that should keep it as is? -- Sajendra

Category

Why is it in the category "Unsolved problems in physics"?

Quantum Theory as it is now is not so much as unsolved as in unsatisfactory. There is no dyanmic in terms of "collapsing wave funtions" into the eigenstates during measurement. Its pretty flimsy when it talks about the interaction of "quantum and classical" systems. These questions are really statistical mechanics problems but the source is in quantum mechanics. Overall Quantum definatly predicts experiments accurately in its regime.

You could say its unsolved in the sense theres no Quantum theory of gravity. However that quantum is really Quantum Field Theory and not Quantum Mechanics.

--Blckavnger 19:59, 17 November 2006 (UTC)

the article quantum teleportation

i have posted here because i think no one will respond at the discussion there

it says: Indistinguishability Let's say that Alice has a rubidium atom (the element physicists in this field like to use for their experiments), which is in its ground state, and Bob also has such an atom, as well in its ground state. It is important to see that these two atoms are indistinguishable; that means that there really is no difference between them.

If Alice and Bob had, say, two glass balls, which exactly look alike, and they exchanged them, then something would change. If you had a powerful microscope, you could certainly find some difference between the two balls. For atoms of the same kind and in the same quantum state, however, there really is no difference at all. The physical situation with Alice having the first atom and Bob the second is exactly the same as vice versa.1 In a certain sense, it is even wrong to say that the two atoms have any individuality or identity. It would be more appropriate to say that the two locations in space both have the property that the fundamental quantum fields have those values which define the ground state of the rubidium atom.

how can rubidium atoms be in the same quantum state? are they like helium 4 or something? or does the exclusion principle apply only through a maximum distance? sorry for the stupid question but im the person who asked the spin so you would know i dunno much

-protecter

plain English section needed!

I am an (ex-)physicist, but also a writer, and frankly the article on Quantum Mechanics causes me pain to read, or at least the introduction. There should be a plain English paragraph at the start for the non-technical reader who has stumbled here or just wants a quick idea what's going on. This article reads like it was written by physicists for physicists. This is an encyclopaedia, not the Feyman lectures!

In fact, I propose that every technical article of any length should have a plain English paragraph. Feynman said (I'm paraphrasing) that if you can't explain something to a 1st year college student then you don't understand it fully. We need a paragraph for an even lower level than this, in essence making the absolute minimum assumptions of the reader's prior knowledge.

Alternatively, I propose that long technical articles could have a separate "explanatory" article written in the simplest language possible.

Here is a quick shot:

"Quantum Mechanics is a theory in physics which primarily tries to explain how extremely small bodies, such as atoms, behave. Scientists generally agree that it is a very accurate and successful theory and it has very important applications in today's world as all electronic devices, such as computer chips, depend on Quantum Mechanics is some way. It is also important in understanding how large objects such as stars and the Universe as a whole are the way they are.

Despite how successful Quantum Mechanics is at explaining what we see, it does it does have some controversial elements. For example, the behaviour of microscopic objects is very different from the behaviour of everyday objects, and some of its results appear to contradict the Theory of Relativity." Paulc1001 13:03, 1 October 2005 (UTC)

To paraphrase Eric Cornell, we might add to "extremely small bodies" the phrase "wavelike entities". Their wavelike character becomes become more and more apparent as we explore the regimes of extremely low temperatures. In other words, their edges cease to become distinct but merge into each other, even at macroscopic scale. For example, in his public lectures he displays a picture of rubidium Bose Einstein condensate at millimeter scale for a collection of about a million Rb atoms in a magnetic trap, at a millionth of a Kelvin, with a common wave function. A wave function 1 millimeter across! (He actually characterized it as a picture of a wave function squared.) I am trying to ascertain the license conditions for his images, as he works for NIST. They would be a dramatic addition to the QM article as examples of wave functions. Ancheta Wis 15:12, 15 October 2005 (UTC)

Meh. The fact that you can see quantum mechanics on a macroscopic scale in BEC's is nice but hardly new. BEC's are basically another type of superfluid. We've had experimental evidence of those for around sixty or ninety years, depending on how you count. -- CYD

The distribution of the superfluid vortices in Cornell's image is highly regular, beautiful even. I am trying to find a good public image for others to see. The image is nontrivial. Ancheta Wis 10:16, 24 October 2005 (UTC)

Again, the vortices that you see in BEC are exactly the same as vortices in superfluid helium and superconductors (in fact, the ability to form vortices is "built-in" to the idea of a superfluid). Here's an image of vortices in a superconductor from 1967: [2] -- CYD

I tried to read this to learn more on the topic and gave up. I strongly suggest a very simplified page in the simple english wiki.

One thing that is wrong in the proposed Plain English description is the characterization of atoms as "extremely small bodies": common experience would make those bodies 'little hard ball bearings' but that is exactly the point of the BEC discussion above -- they are not little -- they can be 1 millimeter across, acting 'together' in an extremely coordinated way -- millions of atoms (but not little balls, more like waves, all behaving identically) together. The Plain English discussion needs to integrate the Heisenberg principle, so that the little ball picture can be left behind. Ancheta Wis 10:06, 29 October 2005 (UTC)

The discussion above exemplifies bullets ii) and iii) in the 3rd paragraph in the introduction to the article. 10:35, 29 October 2005 (UTC)

Spatial quantization

I wonder if someone can explain how we know that energy states, momentum and various other quantities are quantized, yet space is not. It has often seemed to me that if we are unable to unify gravity fully with quantum mechanics, then one or other of them must be wrong in some fundamental manner. What would the consequences be on physical theory if in fact the universe was fully quantized? And would there be an easy test to prove that the universe is not in such a state? Has anyone done any work in this area?

Yeah. Plain English Please

I'm a general studies student and I'm writing an anthropology paper about technology in post-modern society. I'm pretty sure quantum physics is a big part of this but I couldn't understand a thing in this article. Some plain 'explain it to a novice' language would be really nice. Also that this article has recieved so much attention is great but it doesn't help the lay person and in fact it makes one feel kind of intellectually inadequate.

No slight is intended. In a nutshell, our common-sense ideas about place (ie position in space) would have to change if we truly were to integrate the knowledge of QM into our current civilization; you can model the world at many levels; look at History of science for an overview in the broadest terms. In fact Newtonian physics (1700) (approximating the world with hard spheres and rigid bodies) is adequate for understanding a huge part of our civilization. We are just now reaping the benefits of Maxwell's equations (1865) with the electronic circuits of today ( not derived from QM). Look at solid state physics (which uses some QM) if you want to see the physical basis of our understanding of microelectronic technology. The precision and repeatability of our integrated circuits are applications of optics, especially photography and cameras, and the ideas behind the printing press (1041) and lithography (1798). But laser physics (1960) and physics of condensed matter (1900-present) is just starting to reap the benefits of the QM viewpoint. In other words, you don't need to understand the QM viewpoint until you start studying physics, engineering and especially chemistry. And you don't meet too many people who worry about the nature of spacetime or matter on an everyday basis. It truly is a subject for specialized study, in our current civilization. --Ancheta Wis 23:25, 26 November 2005 (UTC)

QM, the uncertainty principle in all of its quantum weirdness

I wrote this illustration on the "uncertainty principle" talk and wanted to share. Also, I haven't looked at this article on QM in awhile and it has improved, but still may be too complicated in the intro. I'm going to "think on it".

To explain QM, especially the uncertainty principle, I will use a simplified anthropomorphic illustration of electrons in orbits around the atom applying the principles of uncertainty and QM to show how "strange" strange really is. First, let's start with the retained QM features of the Bohr atom model. Imagine an electron as a person, in fact, say you are the electron and you are running around a circular track about 10 feet wide. There is another inside track in further from your track by another few yards. This inside track is also 10 feet wide. There is a refreshment stand at the center of the track which is the nucleus and although you are attracted to it, the probability of you ever being able to get to the refreshment stand is zero. No can do. You are using up more energy to do laps running on the outside track, so you want to move to the inside track. However, the probability of you being able to cross those few yards to the inside track is zero. Therefore, you pull out your handy triquarter and say, "Beam me up Scotty," and you are instantaneously transported to the inside track. (quantum leaping) Another weird thing is that if someone is looking at you (but not measuring where you are), they think they have very blurred vision because you seem to be blurred across the whole ten feet of the track. Most of your body is concentrated at your position, but the rest of you is stretched out across the track. (uncertainty) Now there is another guy who comes along and wants to run on the inside track with you. You look at him and you see that he is identical to you in every way. In fact, no one looking at either of you can ever tell you apart. (indistinguishable particles) Now he starts running on the inside track with you but in the opposite direction. (spin) He is also spread out over the 10 foot width of the track and is fuzzier and less distinct toward the edges of the track. All of a sudden, you decide to turn around and run in the same direction he is running. But as you turn around, he turns around too as if reading your mind. This happens every time. (quantum entanglement) --- I could go on, but this should be weird enough. The true facts are that the track would describe a sphere and you would be stretched out all over the sphere at once which is even harder to imagine. Not only that, but you would be standing still (standing wave) and moving at the same time (angular momentum). That is why Bohr said "if you don't think QM is strange, you haven't understood a single word."

I love what Einstein had to say about all this:

• (after Heisenberg's 1927 lecture) "Marvelous, what ideas the young people have these days. But I don't believe a word of it."
• "The Heisenberg-Bohr tranquilizing philosophy - or religion? - is so delicately contrived that, for the time being, it provides a gentle pillow for the true believer from which he cannot very easily be aroused. So let him lie there.

Further, the fact that Einstein didn't like uncertainty didn't mean he wasn't still a brilliant genius. In fact, the challenges that Einstein brought to QM have transformed it and tweaked it and refined it.

My personal favorite anachronistic quote about QM is the ironic fact that it came out of Copenhagen in Denmark and Shakespeare said in Hamlet as if speaking of QM itself:

• "There is something rotten in the state of Denmark...There are more things in heaven and earth, Horatio, Than are dreamt of in your philosophy."

--Voyajer 16:51, 23 December 2005 (UTC)

It is much easier and much more physical to imagine the electron in the atom to be not some tiny point jumping from place to place or orbiting around (there are no orbits, there are orbitals), but to imagine the electron being an occupation of an extended orbital and an orbital being a vibrating wave confined to the neighbourhood of the nucleus by its attracting force. That's why Chladni's figures of acoustics and the normal modes of electromagnetic waves in a resonator are such a good analogy for the orbital pictures in quantum physics. Quantum mechanics is a lot less weird if you see this analogy. The step from electromagnetic theory (or acoustics) to quantum theory is much easier than the step from point mechanics to quantum theory, because in electromagnetics you already deal with waves and modes of oscillation and solve eigenvalue equations in order to find the modes. You just have to treat a single electron like a wave, just in the same way as light is treated in classical electromagnetics.

In this picture, the only difference between classical physics and quantum physics is that in classical physics you can excite the modes of oscillation to a continuous degree, called the classical amplitude, while in quantum physics, the modes are "occupied" discretely. -- Fermionic modes can be occupied only once at a given time, while Bosonic modes can be occupied several times at once. Particles are just occupations of modes, no more, no less. As there are superpositions of modes in classical physics, you get in quantum mechanics quantum superpositions of occupations of modes and the scaling and phase-shifting factors are called (quantum) amplitudes. In a Carbon atom, for example, you have a combination of occupations of 6 electronic modes of low energy (i.e. frequency). Entangled states are just superpositions of combinations of occupations of modes. Even the states of quantum fields can be completely described in this way (except for hypothetical topological defects).

As you can choose different kinds of modes in acoustics and electromagnetics, for example plane waves, spherical harmonics or small wave packets, you can do so in quantum mechanics. The modes chosen will not always be decoupled, for example if you choose plane waves as the system of acoustic modes in the resonance corpus of a guitar, you will get reflexions on the walls of modes into different modes, i.e. you have coupled oscillators and you have to solve a coupled system of linear equations in order to describe the system. The same is done in quantum mechanics: different systems of eigenfunctions are just a new name for the same concept. Energy eigenfunctions are decoupled modes, while eigenfunctions of the position operator (delta-like wavepackets) or eigenfunctions of the angular momentum operator in a non-spherically symmetric system are usually strongly coupled.

What happens in a measurement depends on the interpretation: In the Copenhagen interpretation you need to postulate a collapse of the wavefunction to some eigenmode of the measurement operator, while in Everett's Many-worlds theory an entangled state, i.e. a superposition of occupations of modes of the observed system and the observing measurement apparatus, is formed.

--DenisDiderot 21:07, 23 December 2005 (UTC)

• • Thanks for your unnecessary explanation. I am well versed in physics. My analogy was meant to be humorous and over-simplified.--Voyajer 21:12, 23 December 2005 (UTC)

Please don't feel insulted by my clarification which adresses many other readers as well. Most beginners are confused and demoralized when the weirdness of quantum mechanics is overemphasized and they are confronted with lots of contradicting statements. --DenisDiderot 21:29, 23 December 2005 (UTC)

Au contraire, I am not insulted. I just think you don't have a sense of humor. My colleagues found my analogy highly amusing.

What does bother me though is that you think your explanation above is for beginners in physics or beginners in anything for that matter. I would think you would have to have a pretty heavy knowledge of waves, acoustics, and optics to understand your analogy at all. You would need to understand the concept of standing waves as normal modes of bounded systems such as harmonics and the quality of sound. You would need to understand the significance of Chladni's figures. You would need to understand ultrasonic and infrasonic waves. You would need to understand the concept of waves in media like transverse waves in a uniform string, gravity waves and ripples, superposition of waves such as in linear homogeneous equations and nonlinear superposition. Also, you wouldn't be using the terms fermionic and bosonic to beginners and using the terms eigenvalues and eigenfunctions to a neophyte in physics is ludicrous. In other words, your so-called explanation for "beginners" appears simply absurd and conveys the idea that you are simply trying to make a display of your erudition. If you really want to help the beginner, then you should describe in detail the idea of a standing wave, why we view the electron as a standing wave, what an orbital actually is, why an electron is said to be an occupation of an orbital, and the basics of wave-particle duality. Of course, that is just my opinion. It appears to me that much of the "talk" here is by people complaining that everyone is answering questions and explaining things in a pseudo-intellectual fashion not for the edification of the beginner but simply to show off. Of course, all of this is just my opinion, so take it for what it's worth.--Voyajer 00:36, 24 December 2005 (UTC)

Your way to discuss things is obviously highly aggressive, and I wonder what it is that makes you so furious and arrogant. I'll just ignore any further aggressive remarks on your part. Maybe it is you who needs some sense of tolerance and humour (humour does not mean forcing other people to laugh about your jokes).

I have a long experience in explaining quantum mechanics to students the way described above (of course, the text given above is just a sketch), and I found it to be highly successful. Even children can easily grasp the concept of waves and of superpositions of waves, and it is a lot of fun for them to see Chladni's figures. You can do many experiments with standing and propagating waves without any complicated instrumentation, and acoustics is interesting in itself. Much of this is already common knowledge at the age of 12, and in Wikipedia, you can read about all this if you follow the links I provided. The concepts of fermionic and bosonic occupations are defined by the sentence given above, and they are easily grasped by students after delving a little further into some examples and explaining the Pauli exclusion principle and stimulated emission in this context. As soon as the students have grasped the picture and have overcome the prejudice that the electron had to be some pointlike object as they see the orbital to be quite extended, all the weirdness disappears. Of course, many questions arise -- as is always the case when people are bursting with curiosity -- and I'm happy to answer them, because if people are demoralized and think quantum mechanics is just some incomprehensible mess, they cease asking questions.

--DenisDiderot 11:07, 24 December 2005 (UTC)

Not to be annoying; but I'm not a neophyte in quantum mechanics (although I'm not a physicist either), and I had to read your statement twice over, and with the care of reading a college textbook to understand what you were trying to say. And Voyajer is right; using the word eigenvalue for anyone without knowledge of linear algebra, let alone for a total novice in a field, is an improper approach. Nor can you expect someone without a mathematical, engineering, or scientific background to understand 'phase-shifts'. Words like 'Bosonic'--even if explained--will probably throw most people off, and force them to re-read the sentence to understand your prose. Jargon like 'system of linear equations', 'spherical harmonics', and the like don't help out either; nor does the fact that one would have to click on numerous links just to understand some of the ideas you use. My Two Cents. 69.84.100.123 02:25, 28 December 2005 (UTC)Don

It was just a sketch of the main ideas of how such an explanation for beginners (including quantum field theory) avoiding all the weirdness could look like. See Quantum mechanics explained for more details. Feel free to ask questions on the talk page.

--DenisDiderot 02:30, 28 December 2005 (UTC)